On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of SLn

Dhillon, Ajneet

Canadian journal of mathematics, Tome 58 (2006) no. 5, pp. 1000-1025

Résumé

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 Poincaré 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 $\text{S}{{\text{L}}_{n}}$ is one.

Détail

DOI : 10.4153/CJM-2006-038-8

Mots-clés : 14H, 14L

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