Publications

[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), to appear in Progress in Mathematics, Birkhäuser, (2007)

[11] Arithmetic geometry, Proceedings of the Clay Summer School Göttingen 2006, (with H. Darmon and B. Hassett), in preparation

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


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 Ga^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)

[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), 70 pp., to appear in GAFA

[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 Mathematics, 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, 1-24, (2008)

[47] Potential density of rational points for K3 surfaces over function fields, (with B. Hassett), 16 pp., to appear in Amer. Journ. of Math.

[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), 22 pp., (2006)

[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), 16 pp., to appear in Inventiones Math.

[54] Brauer-Manin obstructions for integral points, (with A. Kresch), 7 pp., (2007)

[55] Moving and ample cones of holomorphic symplectic fourfolds, (with B. Hassett), 19 pp., (2007)

[56] A Torelli theorem for curves over finite fields, (with F. Bogomolov and M. Korotiaev), 50 pp., (2008)

[57] Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces, (with B. Hassett), 26 pp., (2008)



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)