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The failure of Kodaira vanishing for Fano varieties, and terminal singularities that are not Cohen-Macaulay (17 pages), pdf.

Recent progress on the Tate conjecture (17 pages), pdf, Bull. Amer. Math. Soc. 54 (2017), 575-590.

Hodge theory of classifying stacks (40 pages), pdf, to appear in Duke Math. J..

Essential dimension of the spin groups in characteristic 2 (16 pages), pdf, to appear in Commentarii Mathematici Helvetici.

Rationality does not specialize among terminal varieties (3 pages), pdf, Math. Proc. Camb. Phil. Soc. 161 (2016), 13-15.

The integral cohomology of the Hilbert scheme of two points (17 pages), pdf, Forum of Mathematics, Sigma 4 (2016), e8, 20 pp.

Adjoint functors on the derived category of motives (18 pages), pdf, to appear in J. Inst. Math. Jussieu.

Hypersurfaces that are not stably rational (10 pages), pdf, J. Amer. Math. Soc. 29 (2016), 883-891.

Complex varieties with infinite Chow groups modulo 2 (11 pages), pdf, Annals of Mathematics 183 (2016), 363-375.

The motive of a classifying space (44 pages), pdf, Geometry and Topology 20-4 (2016), 2079-2133.

Group Cohomology and Algebraic Cycles. Cambridge (2014).

Hodge structures of type (

Chow groups, Chow cohomology, and linear varieties (24 pages), pdf, Forum of Mathematics, Sigma 2 (2014), e17 (25 pages).

On the integral Hodge and Tate conjectures over a number field (11 pages), pdf, Forum of Mathematics, Sigma 1 (2013), e4 (13 pages).

Symmetric differentials and the fundamental group (14 pages), by Y. Brunebarbe, B. Klingler, and B. Totaro, pdf, Duke Math. J. 162 (2013), 2797-2813.

Pseudo-abelian varieties (28 pages), pdf, Ann. Sci. Ecole Norm. Sup. 46 (2013), 693-721.

Line bundles with partially vanishing cohomology (24 pages), pdf, J. Eur. Math. Soc. 15 (2013), 731-754.

Algebraic surfaces and hyperbolic geometry (19 pages), pdf, in Current Developments in Algebraic Geometry, ed. L. Caporaso, J. McKernan, M. Mustata, and M. Popa, MSRI Publications 59, Cambridge (2012), 405-426.

Jumping of the nef cone for Fano varieties (17 pages), pdf, J. Alg. Geom. 21 (2012), 375-396.

The ACC conjecture for log canonical thresholds (after de Fernex, Ein, Mustata, Kollár) (15 pages), pdf, Séminaire Bourbaki, vol. 2009/2010. Astérisque no. 339 (2011), exp. no. 1025, 371-385.

The cone conjecture for Calabi-Yau pairs in dimension two (19 pages), pdf, Duke Math. J. 154 (2010), 241-263.

Moving codimension-one subvarieties over finite fields (17 pages), pdf, Amer. J. Math. 131 (2009), 1815-1833.

Birational geometry of quadrics (19 pages), pdf, Bull. Soc. Math. France 137 (2009), 253-276.

Hilbert's fourteenth problem over finite fields, and a conjecture on the cone of curves (26 pages), pdf, Compos. Math. 144 (2008), 1176-1198.

Algebraic topology, Princeton Companion to Mathematics, ed. T. Gowers, Princeton (2008), 383-396.

Birational geometry of quadrics in characteristic 2 (17 pages), pdf, J. Alg. Geom. 17 (2008), 577-597.

Euler and algebraic geometry (19 pages), pdf, Bull. Amer. Math. Soc. 44 (2007), 541-559.

The automorphism group of an affine quadric (9 pages), pdf, Math. Proc. Camb. Phil. Soc. 143 (2007), 1-8.

The elliptic genus of a singular variety (survey paper, 5 pages), pdf, in Elliptic Cohomology, ed. H. Miller and D. Ravenel, LMS Lecture Note Series 342, Cambridge (2007), 360-364.

The torsion index of E

The torsion index of the spin groups (34 pages), pdf, Duke Math. J. 129 (2005), 249-290.

The resolution property for schemes and stacks (23 pages), pdf, J. Reine Angew. Math. 577 (2004), 1-22.

The curvature of a Hessian metric (21 pages), pdf, Int. J. Math. 15 (2004), 369-391.

Splitting fields for E

Curvature, diameter, and quotient manifolds (12 pages), pdf, Mathematical Research Letters 10 (2003), 191-203.

Non-injectivity of the map from the Witt group of a variety to the Witt group of its function field (11 pages), pdf, J. Inst. Math. Jussieu 2 (2003), 483-493.

Complexifications of nonnegatively curved manifolds (25 pages), pdf, J. Eur. Math. Soc. 5 (2003), 69-94.

Towards a Schubert calculus for complex reflection groups (10 pages), pdf, Math. Proc. Camb. Phil. Soc. 134 (2003), 83-93.

Cheeger manifolds and the classification of biquotients (41 pages), pdf, J. Diff. Geom. 61 (2002), 397-451.

Topology of singular algebraic varieties (9 pages), pdf, in Proceedings of the International Congress of Mathematicians (Beijing, 2002), Vol. 1, 533-541.

The topology of smooth divisors and the arithmetic of abelian varieties (14 pages), pdf, Michigan Mathematics Journal 48 (2000), 611-624.

Chern numbers for singular varieties and elliptic homology (33 pages), dvi, pdf, Annals of Mathematics 151 (2000), 757-791.

Euler characteristics for

The Chow ring of a classifying space (33 pages), pdf, in Algebraic K-Theory, ed. W. Raskind and C. Weibel, Proceedings of Symposia in Pure Mathematics, v. 67, American Mathematical Society, 1999, 249-281.

Torsion algebraic cycles and complex cobordism (33 pages), pdf, J. Amer. Math. Soc. 10 (1997), 467-493.

Projective resolutions of representations of GL(n) (12 pages), dvi, pdf, J. Reine Angew. Math. 482 (1997), 1-13.

Configuration spaces of algebraic varieties (13 pages), pdf, Topology 35 (1996), 1057-1067.

Tensor products in

Cohomology of semidirect product groups (6 pages), dvi, pdf, J. Algebra 182 (1996), 469-475.

Homology operations on a new infinite loop space, pdf, Trans. Amer. Math. Soc.347 (1995), 99-110.

Initial ideals, Veronese subrings, and rates of algebras (18 pages), dvi, pdf, by D. Eisenbud, A. Reeves, and B. Totaro, Adv. Math. 109 (1994), 168-187.

Tensor products of semistables are semistable, pdf, in Geometry and Analysis on Complex Manifolds, Festschrift for Professor S. Kobayashi's 60th Birthday, ed. T. Noguchi, J. Noguchi, and T. Ochiai, World Scientific Publ. Co., Singapore, 1994, pp. 242-250.

A sketch of Lie's work on differential invariant theory, in Sophus Lie Memorial Conference (Oslo, 1992): Proceedings, ed. O. A. Laudal and B. Yahren, Scandinavian University Press, 1994, pp. 99-114.

The total Chern class is not a map of multiplicative cohomology theories, Math. Zeit. 212 (1993), 527-532.

Affine varieties and Stein manifolds, Int. J. Math. 2 (1991), 563-566.

Space curves with nonzero torsion, Int. J. Math. 1 (1990), 109-117.

The cohomology ring of the space of rational functions, pdf, MSRI preprint, 1990.

Milnor K-theory is the simplest part of algebraic K-theory, pdf (13 pages), Ph.D. thesis, University of California, Berkeley, 1989; K-Theory 6 (1992), 177-189.