Riemann-Roch Theorems for Deligne-Mumford Stacks
Algebraic Geometry
2007-05-23 v2
Abstract
The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. To this end, we introduce a "cohomology with coefficients in representations" and a Chern character, and we prove a Grothendieck-Riemann-Roch theorem for the Riemann-Roch transformation it defines. As a corollary we obtain an Hirzebruch-Riemann-Roch formula for the Euler characteristic of a coherent sheaf, and some formulas for the different topological Euler characteristics of complex algebraic stacks.
Cite
@article{arxiv.math/9803076,
title = {Riemann-Roch Theorems for Deligne-Mumford Stacks},
author = {B. Toen},
journal= {arXiv preprint arXiv:math/9803076},
year = {2007}
}
Comments
French, 47 pages, accents correction