Local-global principles for Galois cohomology

David Harbater, Julia Hartmann, Daniel Krashen

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

This paper proves local-global principles for Galois cohomology groups over function fields F of curves that are defined over a complete discretely valued field. We show in particular that such principles hold for Hn(F, ℤ/mℤ(n-1)), for alln > 1. This is motivated by work of Kato and others, where such principles were shown in related cases for n D 3. Using our results in combination with cohomological invariants, we obtain local-global principles for torsors and related algebraic structures over F . Our arguments rely on ideas from patching as well as the Bloch-Kato conjecture.

Original languageEnglish (US)
Pages (from-to)215-253
Number of pages39
JournalCommentarii Mathematici Helvetici
Volume89
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Arithmetic curves
  • Cohomological invariants
  • Galois cohomology
  • Local-global principles
  • Patching

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