Localglobal principles for Galois cohomology
Abstract
This paper proves localglobal 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 $H^n(F, Z/mZ(n1))$, 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 localglobal principles for torsors and related algebraic structures over $F$. Our arguments rely on ideas from patching as well as the BlochKato conjecture.
 Publication:

arXiv eprints
 Pub Date:
 August 2012
 arXiv:
 arXiv:1208.6359
 Bibcode:
 2012arXiv1208.6359H
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  Rings and Algebras;
 11E72;
 13F25;
 14H25 (Primary) 12G05;
 20G15 (Secondary)
 EPrint:
 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