Quasi-parabolic Siegel Formula

Nitin Nitsure

Quasi-parabolic Siegel Formula

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: Nitin Nitsure

Abstract

The result of Siegel that the Tamagawa number of $SL_r$ over a function field is 1 has an expression purely in terms of vector bundles on a curve, which is known as the Siegel formula. We prove an analogous formula for vector bundles with quasi-parabolic structures. This formula can be used to calculate the Betti numbers of the moduli of parabolic vector bundles using the Weil conjucture.

Keywords

Siegel formula Tamagawa number vector bundles quasi-parabolic structures Betti numbers Weil conjectures

Cite

@article{arxiv.alg-geom/9503001,
  title  = {Quasi-parabolic Siegel Formula},
  author = {Nitin Nitsure},
  journal= {arXiv preprint arXiv:alg-geom/9503001},
  year   = {2008}
}

Comments

LaTeX, 6 pages. Reason for re-submission : A factor that was missing in the first version is now included in the formula

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