Local-global principles for Galois cohomology

David Harbater; Julia Hartmann; Daniel Krashen

Local-global principles for Galois cohomology

Number Theory 2013-04-11 v2 Algebraic Geometry Rings and Algebras

Authors: David Harbater , Julia Hartmann , Daniel Krashen

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 $H^n(F, Z/mZ(n-1))$ , for all $n>1$ . This is motivated by work of Kato and others, where such principles were shown in related cases for $n=3$ . 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.

Keywords

local-global principles Galois cohomology function fields discretely valued field torsors cohomological invariants patching Bloch-Kato conjecture

Cite

@article{arxiv.1208.6359,
  title  = {Local-global principles for Galois cohomology},
  author = {David Harbater and Julia Hartmann and Daniel Krashen},
  journal= {arXiv preprint arXiv:1208.6359},
  year   = {2013}
}

Comments

32 pages. Some changes of notation. Statement of Lemma 2.4.4 corrected. Lemma 3.3.2 strengthened and made a proposition. Some proofs modified to fix or clarify specific points or to streamline the presentation

Local-global principles for Galois cohomology

Abstract

Keywords

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