Refinements to patching and applications to field invariants
Rings and Algebras
2018-05-11 v3 Algebraic Geometry
Abstract
We introduce a notion of refinements in the context of patching, in order to obtain new results about local-global principles and field invariants in the context of quadratic forms and central simple algebras. The fields we consider are finite extensions of the fraction fields of two-dimensional complete domains that need not be local. Our results in particular give the u-invariant and period-index bound for these fields, as consequences of more general abstract results.
Cite
@article{arxiv.1404.4349,
title = {Refinements to patching and applications to field invariants},
author = {David Harbater and Julia Hartmann and Daniel Krashen},
journal= {arXiv preprint arXiv:1404.4349},
year = {2018}
}
Comments
44 pages. We renumbered results to be consistent with the numbering in the published version. We added a needed hypothesis to Corollary 4.13 that was missing from the published version