Simplicial Chern–Weil theory for coherent analytic sheaves, part II

Chern Classes in Deligne Cohomology for Coherent Analytic Sheaves

In this article, we construct Chern classes in rational Deligne cohomology for coherent sheaves on a smooth compact complex manifold. We prove that these classes satisfy the functoriality property under pullbacks, the Whitney formula and the Grothendieck-Riemann-Roch theorem for an immersion. This answers the question of proving that if F is a coherent sheaf of rank i on X, the topological Cher...

Stiefel-whitney Classes for Coherent Real Analytic Sheaves

We develop Stiefel-Whitney classes for coherent real analytic sheaves and investigate their applications to analytic cycles on real analytic manifolds.

Descent for Coherent Sheaves on Rigid-analytic Spaces

If one assumes k to have a discrete valuation, then descent theory for coherent sheaves is an old result of Gabber. Gabber’s method was extended to the general case by Bosch and Görtz [BG]. Our method is rather different from theirs (though both approaches do use Raynaud’s theory of formal models [BL1], [BL2], we use less of this theory). We think that our approach may be of independent interes...

Linear Koszul duality, II: coherent sheaves on perfect sheaves

In this paper we continue the study (initiated in [MR1]) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting, and prove its compatibility with morphisms of vector bundles and base change.

Homotopy theory of simplicial sheaves in completely decomposable topologies