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On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of $\operatorname{SL}_n$ |
Canad. J. Math. 58(2006), 1000-1025
Published:2006-10-01
Printed: Oct 2006
Printed: Oct 2006
- Ajneet Dhillon
Abstract
We compute some Hodge and Betti numbers of the moduli space of stable rank $r$,
degree $d$ vector bundles on a smooth projective curve. We
do not assume $r$ and $d$ are coprime.
In the process we equip the cohomology of an arbitrary algebraic stack with a
functorial mixed Hodge structure. This Hodge structure is
computed in the case of the moduli stack of rank $r$, degree
$d$ vector bundles on a curve. Our methods also yield a formula
for the Poincar\'e
polynomial of the moduli stack that is valid over any
ground field. In the last section we use the previous sections
to give a proof that the Tamagawa number of $\sln$ is one.
| MSC Classifications: |
14H - unknown classification 14H 14L - unknown classification 14L |