Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford.

Bertrand Toen (1)

1 LEP - Laboratoire Émile Picard

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.

Domaines: Géométrie algébrique [math.AG]

Bertrand Toen. Théorèmes de Riemann-Roch pour les champs de Deligne-Mumford.. K-Theory, 1999, 18 (1), pp.33-76. ⟨10.1023/A:1007791200714⟩. ⟨hal-00773032⟩