The Moduli Spaces of Vector Bundles over an Algebraic Curve.
The Monodromy of a Degenerating Family of Curves.
The Mukai pairing. I: A categorical approach.
The multipliers of similitudes and the Brauer group of homogeneous varieties.
The Mumford conjecture
The Mumford Conjecture asserts that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra on the Mumford-Morita-Miller characteristic classes; this can be reformulated in terms of the classifying space derived from the mapping class groups. The conjecture admits a topological generalization, inspired by Tillmann’s theorem that admits an infinite loop space structure after applying Quillen’s plus construction. The text presents the proof by Madsen and...
The Néron-Severi group and the mixed Hodge structure on H2.
The Normal Bundle of a Curve on a Quadric.
The overconvergence of morphisms of etale -spaces on a local field
The -adic local monodromy theorem for fake annuli
The Picard Group of a Quasi-Bundle.
The Positvity of the Chern Classes of an Ample Vector Bundle.
The projectivity of the moduli space of stable curves, II: The stacks M...
The projectivity of the moduli space of stable curves, III: The line bundles on M..., and a proof of the projectivity of M... in characteristic 0.
The Quadratic Schur Subgroup over Local and Global Fields.
The rank of étale cohomology of varieties over -adic or number fields
The rational homotopy theory of smooth, complex projective varieties
The reciprocity obstruction for rational points on compactifications of torsors under tori over fields with global duality.
The relative Riemann-Roch theorem from Hochschild homology.
The scheme of morphisms from an elliptic curve to a Grassmannian
The six operations for sheaves on Artin stacks I: Finite coefficients
In this paper we develop a theory of Grothendieck’s six operations of lisse-étale constructible sheaves on Artin stacks locally of finite type over certain excellent schemes of finite Krull dimension. We also give generalizations of the classical base change theorems and Kunneth formula to stacks, and prove new results about cohomological descent for unbounded complexes.