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

Bertrand Toen
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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.

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Bertrand Toen. 1999-12-05. K-theory and cohomology of algebraic stacks: Riemann-Roch theorems, D-modules and GAGA theorems. https://arxiv.org/abs/math/9908097

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