Tautological Cycles on Jacobian Varieties
Techniques de construction et théorèmes d'existence en géométrie algébrique III : préschémas quotients
The arithmetic of zero cycles on surfaces with geometric genus and irregularity zero.
The Chow-Witt ring.
The computation of Stiefel-Whitney classes
The cohomology ring of a finite group, with coefficients in a finite field, can be computed by a machine, as Carlson has showed. Here “compute” means to find a presentation in terms of generators and relations, and involves only the underlying (graded) ring. We propose a method to determine some of the extra structure: namely, Stiefel-Whitney classes and Steenrod operations. The calculations are explicitly carried out for about one hundred groups (the results can be consulted on the Internet).Next,...
The Euler characteristic of varieties realized as the complete intersection of toric hypersurfaces.
Torus embeddings, polyhedra, k*-actions and homology [Book]
Transcendence degree of zero-cycles and the structure of Chow motives
In the paper we introduce a transcendence degree of a zero-cycle on a smooth projective variety X and relate it to the structure of the motive of X. In particular, we show that in order to prove Bloch’s conjecture for a smooth projective complex surface X of general type with p g = 0 it suffices to prove that one single point of a transcendence degree 2 in X(ℂ), over the minimal subfield of definition k ⊂ ℂ of X, is rationally equivalent to another single point of a transcendence degree zero over...
Twisted cohomology of the Hilbert schemes of points on surfaces.