Period and index in the Brauer group of an arithmetic surface
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Max Lieblich
Abstract
In this paper we introduce two new ways to split ramification of Brauer classes on surfaces using stacks. Each splitting method gives rise to a new moduli space of twisted stacky vector bundles. By studying the structure of these spaces we prove new results on the standard period-index conjecture. The first yields new bounds on the period-index relation for classes on curves over higher local fields, while the second can be used to relate the Hasse principle for forms of moduli spaces of stable vector bundles on pointed curves over global fields to the period-index problem for Brauer groups of arithmetic surfaces. We include an appendix by Daniel Krashen showing that the local period-index bounds are sharp.
© Walter de Gruyter Berlin · New York 2011
Articles in the same Issue
- Period and index in the Brauer group of an arithmetic surface
- A characterization of freeness by invariance under quantum spreading
- Canonical bases and KLR-algebras
- Ranks of invariant subspaces of the Hardy space over the bidisk
- The Kähler–Ricci flow on Hirzebruch surfaces
- A correction to Hasse's version of the Grunwald–Hasse–Wang theorem
- On the regularized Siegel–Weil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups
Articles in the same Issue
- Period and index in the Brauer group of an arithmetic surface
- A characterization of freeness by invariance under quantum spreading
- Canonical bases and KLR-algebras
- Ranks of invariant subspaces of the Hardy space over the bidisk
- The Kähler–Ricci flow on Hirzebruch surfaces
- A correction to Hasse's version of the Grunwald–Hasse–Wang theorem
- On the regularized Siegel–Weil formula (the second term identity) and non-vanishing of theta lifts from orthogonal groups
