K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems

Abstract

This is the integral text of my thesis. The first part is an expanded version of "Riemann-Roch theorems for Deligne-Mumford stacks", where I deal with Artin stacks over general bases. In the second part, I prove some Riemann-Roch statment for D-modules on Deligne-Mumford stacks, and I also consider the problem of algebraization of analytic stacks.

arXiv comment207 pages, french, author's PhD. thesis. Few details are corrected

References in corpus (4)

• Quotients by Groupoids
• Perverse sheaves on a Loop group and Langlands' duality
• Equivariant intersection theory
• Flexible sheaves

Cited by in corpus (11)

• Orbifold Quantum Riemann-Roch, Lefschetz and Serre
• On the classification of rank two representations of quasiprojective fundamental groups
• The moduli space of multi-scale differentials
• On the $K$-theoretic Hall algebra of a surface
• On degree zero elliptic orbifold Gromov-Witten invariants
• On the Picard group scheme of the moduli stack of stable pointed curves
• General GLSM Invariants and Their Cohomological Field Theories
• A Deligne-Riemann-Roch isomorphism I: Preliminaries on virtual categories
• Equality of the wobbly and shaky loci
• On the essential (p)-dimension of parabolic bundles on a curve
• The Bogomolov-Miyaoka-Yau inequality for stacky surfaces