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

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

1999-08-18

arxiv.org/abs/math/9908097v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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