Period and index in the Brauer group of an arithmetic surface
By Max Lieblich. 2007
67 citations recorded by the source corpus.
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.
Subfields: Geometry and Topology, History, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/04067724239b7c1ab0a57d8d706062e78fc8bc04
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Citations in the corpus
- Stable rationality and conic bundles (2015, unknown): “We start, following Lieblich [26], by producing an extension of β to a smooth compactification of Xsm.”
- Period-index and u-invariant questions for function fields over complete discretely valued fields (2013, result): “We note that our definition of Brp dim(K) is distinct from the one defined by Lieblich in [26] or the one defined by Harbater, Hartmann and Krashen in [14] and [3].”