[1] Rational points on algebraic varieties, (with E. Peyre),
Progress in Mathematics **199**, Birkhäuser, (2001)

[2]
Arithmetic of higher-dimensional algebraic varieties, (with B. Poonen),
Progress in Mathematics **226**, Birkhäuser, (2003)

[3] Mathematisches Institut, Seminars 2003/04, Universitätsverlag Göttingen, (2004)

[4] Geometric methods in algebra and number theory, (with F. Bogomolov),
Progress in Mathematics **235**, Birkhäuser, (2004)

[5] Mathematisches Institut, Seminars 2004, Universitätsverlag Göttingen, (2004)

[6] Mathematisches Institut, Seminars 2004/05, Universitätsverlag Göttingen, (2005)

[7]
Mathematisches Institut,
Summer school *Algebraic groups*,
Göttingen 2005,
Universitätsverlag Göttingen (2007)

[8] Analytic Number Theory / A tribute to Gauss and Dirichlet, (with W. Duke), CMI Proceedings series, AMS, (2007)

[9]
Eisenstein series and
applications, (with W.T. Gan and S. Kudla),
Progress in Mathematics **258**, Birkhäuser, (2008)

[10]
Algebra, Arithmetic and
Geometry - Manin Festschrift, (with Yu. Zarhin),
Progress in Mathematics **269** and **270**, Birkhäuser, (2007)

[11] Arithmetic geometry, Proceedings of the Clay Summer School Göttingen 2006, (with H. Darmon and B. Hassett), CMI Proceedings series, AMS, (2009)

[12] Higher-dimensional geometry over finite fields, Advanced Study Institute 2007 Proceedings, (with D. Kaledin), IOS Press, (2008)

[13]
Mathematisches Institut,
*Trends in mathematics, Courant Colloquium Göttingen*,
(with R. Meyer and Th. Schick), Universitätsverlag Göttingen, (2008)

[14]
Cohomological and geometric
approaches to rationality problems,
(with F. Bogomolov), Progress in Mathematics **282**, Birkhäuser, (2009)

[15] Birational geometry, rational curves, and arithmetic, (with F. Bogomolov and B. Hassett), Springer Verlag, (2013)

[16]
Rational points, rational curves and entire holomorphic curves on projective varieties,
(with C. Gasbarri, S.S.-Y. Lu, and M. Roth), Contemporary Math. **654**, AMS, (2015)

[17]
Algebra, Geometry, and Physics in the 21 Century,
Kontsevich Festschrift,
(with D. Auroux, L. Katzarkov, T. Pantev, and Y. Soibelman),
Progress in Mathematics **324**, Birkhäuser, (2017)

[18]
Geometry over nonclosed fields - Simons Symposium 2015,
(with F. Bogomolov and B. Hassett), Springer Verlag, (2017)

** Research papers**

[1] Rational points of bounded height on Fano varieties
(with J. Franke, Yu. I. Manin),
*Inventiones Math.,* 95, 421-435, (1989)

[2]
Points of bounded height on Del Pezzo surfaces,
(with Yu. I. Manin), * Compositio Math.,* 85(3), 315-332, (1993)

[3]
Rational points of bounded height on compactifications
of anisotropic tori, (with V. Batyrev), *Intern. Math. Research
Notices,* 12, 591-635, (1995)

[4]
Height zeta functions of toric varieties, (with V. Batyrev),
*Algebraic geometry, 5, (Manin's Festschrift), Journ. Math. Sci., * 82,
no. 1, 3220-3239, (1996)

[5]
Rational points on some Fano cubic bundles, (with V. Batyrev),
*C. R. Acad. Sci., Paris,* 323, Ser. I, 41-46, (1996)

[6]
Height zeta functions of twisted products, (with M. Strauch),
*Math. Res. Letters,* 4, 273-282, (1997)

[7]
Manin's conjecture for toric varieties, (with V. Batyrev),
*Journ. of Alg. Geom.,* 7, no. 1, 15-53, (1998)

[8]
Tamagawa numbers of polarized
algebraic varieties, (with V. Batyrev),
*Asterisque, * 251, 299-340, (1998)

[9]
Height zeta functions of toric bundles over flag varieties,
(with M. Strauch), * Selecta Math. (N.S.),* 5, no. 3, 325-396, (1999)

[10]
Tamagawa numbers of diagonal cubic surfaces, (with E. Peyre),
*Math. Comp.,* 70, 367-387, (2001)

[11]
Torseurs arithmetiques et espaces fibres, (with A. Chambert-Loir),
*"Rational points on algebraic varieties", * 37-70,
Progress in Math. 199, Birkhäuser, (2001)

[12]
Rational points on quartics, (with J. Harris),
* Duke Math. Journ.*, 104, no. 3, 477-500, (2000)

[13]
On the density of rational points on elliptic fibrations,
(with F. Bogomolov), *
Journ. Reine und Angew. Math., * 511, 87-93, (1999)

[14]
Density of rational points on Enriques surfaces,
(with F. Bogomolov), * Math. Res. Letters, * 5, 623-628, (1998)

[15]
Fonctions zeta des hauteurs des espaces fibres,
(with A. Chambert-Loir),
*"Rational points on algebraic varieties", * 71-115,
Progress in Math. 199, Birkhäuser, (2001)

[16]
Density of rational points on elliptic K3 surfaces,
(with F. Bogomolov), * Asian Journ. of Math.,* 4, no. 2,
351-368, (2000)

[17]
Points of bounded height on
equivariant compactifications of vector groups I,
(with A. Chambert-Loir), * Compositio Math.,*
124(1), 65-93, (2000)

[18]
Tamagawa numbers of diagonal cubic surfaces of higher rank,
(with E. Peyre),
*"Rational points on algebraic varieties", * 275-305,
Progress in Math. 199, Birkhäuser, (2001)

[19]
Geometry of equivariant compactifications of **G**_{a}^{n},
(with B. Hassett),
* Intern. Math. Research Notices, * 22, 1211-1230, (1999)

[20]
Points of bounded height on
equivariant compactifications of vector groups II,
(with A. Chambert-Loir), * Journ. of Number Theory,
*85, no. 2, 172-188, (2000)

[21]
Rational curves on holomorphic
symplectic fourfolds, (with B. Hassett), *GAFA, *
11, no. 6, 1201-1228, (2001),
Erratum

[22]
Abelian fibrations and rational
points on symmetric products, (with B. Hassett),
*Intern. Journ. of Math.,* 11, no. 9, 1163-1176, (2000)

[23]
On the distribution of points of bounded height on
equivariant compactifications of vector groups,
(with A. Chambert-Loir), * Inventiones Math.,* 148, no. 2,
421-452, (2002)

[24]
Monodromy of elliptic surfaces,
(with F. Bogomolov), * "Galois Groups and
Fundamental Groups"*, (L. Schneps, ed.), 167-181,
MSRI Publications vol. 41, Cambridge Univ. Press, (2003)

[25]
Density of integral points on algebraic varieties,
(with B. Hassett),
*"Rational points on algebraic varieties", * 169-197,
Progress in Math. 199, Birkhäuser, (2001)

[26]
Lagrangian subvarieties of abelian fourfolds, (with F. Bogomolov),
* Asian Journ. of Math.,* 4, no. 1, 19-36, (2000)

[27] Commuting elements in Galois groups of function fields,
(with F. Bogomolov), *"Motives, Polylogarithms and Hodge
theory",* (F. Bogomolov, L. Katzarkov eds.), 75-120,
International Press, (2002)

[28] Distribution of rational points on equivariant compactifications of inner forms of reductive groups, (with J. Shalika and R. Takloo-Bighash), 50 pp., (2001)

[29]
Rationality of moduli of elliptic fibrations with fixed monodromy,
(with F. Bogomolov and T. Petrov), * GAFA*, 12, no. 6, 1105-1160, (2002)

[30]
Simple examples of symplectic four-manifolds with exotic properties,
(with F. Bogomolov), *Acta Appl. Math.*, 75, no. 1-3, 25-28, (2003)

[31]
On the effective cone of the
moduli space of pointed rational curves,
(with B. Hassett),
*"Topology and Geometry"*
(A. J. Berrick, M. C. Leung, X. W. Xu eds.),
*Contemporary Math.*,
314, 83-96, (2002)

[32]
Rational points and automorphic forms,
(with J. Shalika and R. Takloo-Bighash),
*"Contributions to Automorphic Forms, Geometry, and Number Theory"*,
(H. Hida, D. Ramakrishnan, F. Shahidi eds.), 733-742, Johns Hopkins University Press, (2004)

[33]
Height zeta functions of
equivariant compactifications of the Heisenberg group,
(with J. Shalika),
*"Contributions to Automorphic Forms, Geometry, and Number Theory"*,
(H. Hida, D. Ramakrishnan, F. Shahidi eds.), 743-771,
Johns Hopkins University Press, (2004)

[34]
Unramified correspondences,
(with F. Bogomolov), *
"Algebraic Number Theory and Algebraic Geometry"*
(S. Vostokov, Yu. Zarhin eds.), *Contemporary Math. *
300, 17-26, (2002)

[35]
Integral points on punctured abelian surfaces,
(with A. Kresch), *
"Algorithmic number theory", Proceedings of ANTS V, 198-204,* LNCS
2369,
Springer, (2002)

[36]
Integral points and effective cones of moduli spaces of stable maps,
(with B. Hassett), * Duke Math. Journ.*, 120, no. 3, 577-599, (2003)

[37]
Special elliptic fibrations,
(with F. Bogomolov), *Proceedings of the Fano Conference*,
(A. Collino, A. Conte, M. Marchisio, eds.), 223-234, (2004)

[38]
On the arithmetic of Del Pezzo surfaces of degree two, (with A. Kresch),
* Proceedings London Math. Soc.*, (3) 89, 545-569, (2004)

[39]
Reconstruction of function fields, (with F. Bogomolov),
*GAFA*, 18, no. 2, 400-462, (2008)

[40]
Universal torsors and Cox rings,
(with B. Hassett), *"Arithmetic of higher-dimensional
algebraic varieties"*, 149-173, Progress in Math. 226, Birkhäuser, (2003)

[41]
Rational points on compactifications of semi-simple groups of rank 1,
(with J. Shalika and R. Takloo-Bighash),
*"Arithmetic of higher-dimensional
algebraic varieties"*, 205-233, Progress in Math. 226, Birkhäuser, (2003)

[42]
Rational curves and points on K3 surfaces,
(with F. Bogomolov), *Amer. Journ. of Math.*, 127, no. 4, 825-835, (2005)

[43]
Couniformization of curves over number fields,
(with F. Bogomolov), *"Geometric methods in algebra and number theory"*, 43-57,
Progress in Math. 235, Birkhäuser, (2004)

[44]
Weak approximation over function fields, (with B. Hassett), *Inventiones Math.*,
163, no. 1, 171-190, (2006)

[45]
Curves in abelian varieties over finite fields,
(with F. Bogomolov), *Intern. Math. Research Notices*, 4, 233-238, (2005)

[46]
Approximation at places of bad reduction for rationally connected varieties,
(with B. Hassett), *Pure and Applied Math Quarterly,
Bogomolov Festschrift*, 4, no. 3, 743-766, (2008)

[47]
Potential
density of rational points for K3 surfaces over function fields,
(with B. Hassett), *Amer. Journ. of Math.*, 130, no. 5, 1263-1278, (2008)

[48]
Algebraic varieties over small
fields,
(with F. Bogomolov), *Special semester on Arithmetic geometry at Centro Ennio De Giorgi*,
53-71, (2007)

[49]
Universal
torsors over Del Pezzo surfaces and rational points,
(with U. Derenthal), *"Equidistribution in Number theory, An Introduction"*,
(A. Granville, Z. Rudnick eds.),
169-196, NATO Science Series II, **237**, Springer, (2007)

[50]
Rational
points on compactifications of semi-simple groups,
(with J. Shalika and R. Takloo-Bighash),
*Journ. of the AMS*, 20, 1135-1186, (2007)

[51]
Weak approximation for hypersurfaces of low degree,
(with B. Hassett), * Proceedings Symp. Pure Math. AMS*, 80 (2), 937-955, (2009)

[52]
Effectivity of Brauer-Manin obstructions, (with A. Kresch),
*Advances in Math.*,
218, no. 1, 1-27, (2008)

[53]
Log Fano
varieties over function fields of curves, (with B. Hassett),
*Inventiones Math.*, 171, no. 1., 7-21, (2008)

[54]
Brauer-Manin obstructions for integral points, (with A. Kresch),
*Bulletin LMS*, 40, no. 6, 995-1001, (2008)

[55]
Moving and ample cones of holomorphic
symplectic fourfolds, (with B. Hassett),
*GAFA*, 19, no. 4, 1065-1080, (2009)

[56]
A Torelli theorem for curves over finite
fields, (with F. Bogomolov and M. Korotiaev),
*Pure and Applied Math Quarterly,
Tate Festschrift*, 6, no. 1, 245-294, (2010)

[57]
Flops on holomorphic symplectic fourfolds
and determinantal cubic hypersurfaces, (with B. Hassett),
*Journ. Inst. Math. Jussieu*, 6, no. 1, 125-153, (2010)

[58]
On a theorem of Tate,
(with F. Bogomolov), *CEJM*, 6, no. 3, 343-350, (2008)

[59]
Unramified
cohomology of finite groups of Lie type, (with F. Bogomolov and T. Petrov),
*"Rationality problems"*, 55-73, Progress in Math. 282, Birkhäuser, (2009)

[60]
Milnor K_{2} and
field homomorphisms, (with F. Bogomolov), *Surveys in Differential Geometry XIII*, 223-244, (2009)

[61]
Co-fibered products of algebraic
curves, (with F. Bogomolov), *CEJM*, 7, no. 3, 382-386, (2009)

[62]
Igusa integrals and volume asymptotics in analytic and adelic geometry,
(with A. Chambert-Loir), *Confluentes Mathematici*, 2, no. 3, 351-429, (2010)

[63]
Constructing
rational curves on K3 surfaces, (with F. Bogomolov and B. Hassett), *Duke Math. Journ.*, 157, no. 3, 535-550, (2011)

[64]
Intersection numbers of extremal rays on holomorphic symplectic varieties, (with B. Hassett),
*Asian Journ. of Math.*, 14, no. 3., 303-322, (2010)

[65]
Effectivity of Brauer-Manin obstructions on surfaces, (with A. Kresch), *Advances in Math.*,
226, 4131-4144, (2011)

[66] Monodromy and rational curves on holomorphic symplectic varieties, (with B. Hassett), 9 pp., (2009)

[67]
Integral points of bounded height on partial equivariant compactifications
of vector groups, (with A. Chambert-Loir), *Duke Math. Journal*,
161, no. 15, 2799-2836, (2012)

[68]
Reconstruction of higher-dimensional function fields, (with F. Bogomolov),
*Moscow Math. Journal*, 11, no. 2, 185-204, (2011)

[69]
Hodge theory and Lagrangian planes on generalized Kummer fourfolds,
(with B. Hassett), *Moscow Math. Journal*, 13, no. 1, 33-56, (2013)

[70] Integral points of bounded height on toric varieties, (with A. Chambert-Loir), 28 pp., (2010)

[71]
Introduction to birational anabelian geometry, (with F. Bogomolov), in *"Current Developments in Algebraic Geometry"*, (L. Caporaso, J. McKernan, M. Mustata, M. Popa eds.), 17-63, MSRI Publications vol. 59, Cambridge Univ. Press, (2012)

[72]
Characterizing projective spaces on deformations of Hilbert schemes of
K3 surfaces,
(with D. Harvey and B. Hassett), *Comm. Pure and Applied Math.*, 65, no. 2., 264-286, (2012)

[73]
Height zeta
functions of equivariant compactifications of semi-direct
products of algebraic groups, (with S. Tanimoto),
*Contemporary Math.,* 566, 119-157, (2012)

[74]
Integral points of bounded height on compactifications of semi-simple groups,
(with R. Takloo-Bighash), *Amer. Journ. of Math.*, 135, no. 5, 1433-1448, (2013)

[75]
Spaces of sections of quadric surface fibrations over curves,
(with B. Hassett), *Contemporary Math.,* 564, 227-249, (2012)

[76]
Multiple mixing for adele groups and rational points,
(with A. Gorodnik, R. Takloo-Bighash), *Europ. Journ. of Math.*, 1(3), 441-461, (2015)

[77]
Galois theory and projective geometry,
(with F. Bogomolov), *Comm. Pure and Applied Math.*, 66, no. 9, 1335-1359, (2013)

[78]
Effective computation of Picard groups and Brauer-Manin obstructions of degree two K3 surfaces over number fields,
(with B. Hassett and A. Kresch),
*Rendiconti del Circolo Matematico di Palermo*, 62, 137-151, (2013)

[79]
Embedding pointed curves in K3 surfaces, (with B. Hassett),
*Math. Zeitschrift*, 278, Issue 3-4, 927-953, (2014)

[80]
Quartic Del Pezzo surfaces over function fields of curves, (with B. Hassett), * CEJM*, 12(3), 395-420, (2014)

[81]
Balanced line bundles and equivariant compactifications of homogeneous spaces, (with B. Hassett and S. Tanimoto), *Intern. Math. Research Notices,* vol. 2015, no. 15, 6375-6410, (2015)

[82]
Mori cones of holomorphic symplectic varieties of K3 type, (with A. Bayer and B. Hassett), *Ann. Sci. ENS*, (4) 48, no. 4, 941–950, (2015)

[83]
On the moduli space of degree 4 Del Pezzo surfaces, (with B. Hassett and A. Kresch),
* Development of Moduli Theory (Mukai Festschrift), Advanced Studies in Pure Math.*, **69**, 349-386, (2016)

[84]
Universal spaces for unramified Galois cohomology,
(with F. Bogomolov), in *Brauer groups and obstruction problems: moduli spaces and arithmetic*,
(A. Auel, B. Hassett, A. Varilly-Alvarado, and B. Viray eds.), 57-86, Progress in Math. 320, Birkhäuser, (2017)

[85]
Height zeta functions of equivariant compactifications of unipotent groups,
(with J. Shalika), *Comm. Pure and Applied Math.*, 69, no. 4, 693–733, (2016)

[86]
Variation of Neron-Severi ranks of
reductions of K3 surfaces, (with E. Costa), *Experimental Math.*, 23, no. 4, 475–481, (2014)

[87]
Rational points on K3 surfaces and derived equivalence,
(with B. Hassett), in
*Brauer groups and obstruction problems: moduli spaces and arithmetic*,
(A. Auel, B. Hassett, T. Varilly-Alvarado, and B. Viray, eds.), 87-113,
Progress in Math. 320, Birkhäuser,
(2017)

[88]
Balanced line bundles on Fano varieties,
(with B. Lehmann and S. Tanimoto), 37 pp., to appear in *Journ. Reine und Angew. Math.*, (2014)

[89]
Stable rationality and conic bundles,
(with B. Hassett and A. Kresch), *Math. Annalen*, 365(3), 1201-1217, (2016)

[90]
Extremal rays and automorphisms of holomorphic symplectic varieties,
(with B. Hassett), *"K3 surfaces and their moduli"*, (G. Farkas and G. van der Geer, eds.),
73-95, Progress in Math. 315, Birkhäuser, (2016)

[91]
On stable rationality of Fano threefolds and Del Pezzo fibrations,
(with B. Hassett), 21 pp., to appear in *Journ. Reine und Angew. Math.*, (2016)

[92] Stable rationality of quadric surface bundles over surfaces, (with B. Hassett and A. Pirutka), 24 pp., (2016)

[93] A very general quartic double fourfold is not stably rational, (with B. Hassett and A. Pirutka), 16 pp., (2016)

[94] Cubic fourfolds fibered in Del Pezzo surfaces of degree six, (with N. Addington, B. Hassett, and A. Varilly-Alvarado), 19 pp., (2016)

[95] Torsion of elliptic curves and unlikely intersections, (with F. Bogomolov and H. Fu), 19 pp, (2017)

[96]
Intersections of three quadrics in **P**^{7},
(with B. Hassett and A. Pirutka), 18 pp., (2017)

[97] Multiplicative homomorphisms of fields preserving algebraic dependence, (with F. Bogomolov and M. Rovinsky), 30 pp., (2017)

[98] Models of Brauer-Severi surface bundles, (with A. Kresch), 50 pp., (2017)

[99]
Specialization of birational types,
(with M. Kontsevich), 17 pp., (2017)

**Surveys and technical reports **

[1] Rational points and heights, (Russian),
* Proceedings of the XXVIth
All-Union Sci. Stud. Conference
(Novosibirsk, 1988),*
Novosibirsk. Gos. Univ., 80-84, (1988)

[2] Generalised Chatelet varieties, (Russian), *
Proceedings of the conference "Constructive Methods
and Algorithms in Number Theory", *
Academy of Sci. BSSR, Minsk, USSR, 163, (1989)

[3] Arithmetic of algebraic surfaces, Ph.D. Thesis, M.I.T., (1992)

[4] Finite heights and rational points on surfaces,
*Advances in number theory (Kingston, ON, 1991)*, 319--329,
Oxford Sci. Publ.,
Oxford Univ. Press, New York, (1993)

[5] On rational points, *
Proceedings "Intern. Conf. Algebraic Geometry"*, Sendai,
157-172, (1993)

[6]
Rational points on toric varieties, (with V. Batyrev),
*Number theory (Halifax, NS, 1994), CMS Conf. Proc.,* 15,
AMS, Providence, RI, 39-48, (1995)

[7]
Height zeta functions,* Proceedings Arbeitstagung Bonn*, (1997)

[8]
Lectures on height zeta functions of toric varieties,
"Geometry of Toric Varieties",
*Seminaires et Congres*, 6, 227-247, (2002)

[9]
Resolution of singularities,
(with F. Bogomolov), Review of a book by
H. Hauser et al., *Bulletin AMS*, 39, 95-100, (2002)

[10]
Fujita's program and rational points,
*"Higher Dimensional Varieties and Rational Points",*
(K. J. Böröczky, J. Kollár, T. Szamuely eds.),
*Bolyai Society Mathematical Studies *
12, 283-310, Springer Verl., (2003)

[11]
On curve correspondences, (with F. Bogomolov),
*"Communications in Arithmetic Fundamental Groups and Galois Theory"*,
RIMS, 157-166, (2002)

[12]
About the cover: On the distribution of primes - Gauss' tables,
*Bulletin AMS*, 43, 89-91, (2006)

[13] Geometry over nonclosed fields, ICM talk, 15 pp., (2006)

[14]
About the
cover: Invariants,
*Bulletin AMS*, 44, 433-437, (2007)

Minkowski to Hilbert, February 2, 1892,
1,
2,
3,
4
(courtesy of Staats- und
Universitätsbibliothek Göttingen)

[15]
The Felix
Klein protocols, (with E. Chislenko),
*Notices AMS*, 54 (8), 958-968, (2007)

[16] Algebraic varieties with many rational points, Clay Summer School Proceedings, 92 pp., (2008)

[17] Die Felix Klein Protokolle, 11 pp., (2008)

[18]
Geometrie der Zahlen - zum 150. Geburtstag von Hermann Minkowski, *Mitteilungen der DMV*, 22 (4), 228-233, (2014)