On the Cohomology of Moduli of Vector Bundles and the Tamagawa Number of SLn
- 1 October 2006
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 58 (5) , 1000-1025
- https://doi.org/10.4153/cjm-2006-038-8
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 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 SLn is one.Keywords
This publication has 12 references indexed in Scilit:
- Intermediate Jacobians and Hodge structures of moduli spacesProceedings - Mathematical Sciences, 2000
- Borel-Weil-Bott theory on the moduli stack of G -bundles over a curveInventiones Mathematicae, 1998
- The Lefschetz trace formula for algebraic stacksInventiones Mathematicae, 1993
- Nombres de Tamagawa et groupes unipotents en caract ristique pInventiones Mathematicae, 1984
- The Yang-Mills equations over Riemann surfacesPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1983
- Théorie de hodge, IIIPublications mathématiques de l'IHÉS, 1974
- Some Theorems on Actions of Algebraic GroupsAnnals of Mathematics, 1973
- Techniques de descente cohomologiqueLecture Notes in Mathematics, 1972
- Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: IAnnals of Mathematics, 1964
- Imbedding of an abstract variety in a complete varietyKyoto Journal of Mathematics, 1962