| Bertrand Toen Parc Valrose, 06108 Nice Cedex 2 Tel email : toen@math.unice.fr Publications, preprints and notes: Ph. D. Toulouse June 99 (file .dvi 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. K-theory No. 18, 1999 (file .dvi The goal of this paper is to prove Riemann-Roch type theorems for Deligne-Mumford algebraic stacks. For this, 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. Notes sur la G-theorie rationelle des champs de Deligne-Mumford | |
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