Arithmetic aspects of moduli of sheaves on curves

Details Arithmetic aspects of moduli of sheaves on curves Arithmetic aspects of moduli of sheaves on curves

2009-02-03

arxiv.org/abs/0902.0482v3

Mathematics

Algebraic Geometry

History of Brauer-Manin obstruction clarified. To appear in Clay volume on vector bundles in honor of Newstead. Margins/format

Scientific paper

We describe recent work on the arithmetic properties of moduli spaces of stable vector bundles and stable parabolic bundles on a curve over a global field. In particular, we describe a connection between the period-index problem for Brauer classes over the function field of the curve and the Hasse principle for rational points on etale forms of such moduli spaces, refining classical results of Artin and Tate. Submitted to proceedings of a Clay workshop on vector bundles on curves in honor of Newstead.

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