A bound to kill the ramification over function fields

Alena Pirutka

doi:10.1016/j.jalgebra.2012.11.045

A bound to kill the ramification over function fields

Alena Pirutka

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist ⁿ² functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

Original language	English (US)
Pages (from-to)	173-178
Number of pages	6
Journal	Journal of Algebra
Volume	377
DOIs	https://doi.org/10.1016/j.jalgebra.2012.11.045
State	Published - Mar 1 2013

Keywords

Brauer group
Galois cohomology
Period-index problem
Unramified cohomology

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2012.11.045

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title = "A bound to kill the ramification over function fields",

abstract = "Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist n2 functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).",

keywords = "Brauer group, Galois cohomology, Period-index problem, Unramified cohomology",

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N2 - Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist n2 functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

AB - Let k be a field of characteristic zero, let X be a geometrically integral k-variety of dimension n and let K be its field of functions. We prove that, given an element α∈Hm(K,μr⊗m), there exist n2 functions {fi},i=1,...,n2 such that α becomes unramified in L=K(f11/r,...,fn21/r).

KW - Brauer group

KW - Galois cohomology

KW - Period-index problem

KW - Unramified cohomology

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VL - 377

SP - 173

EP - 178

JO - Journal of Algebra

JF - Journal of Algebra

ER -

A bound to kill the ramification over function fields

Abstract

Keywords

ASJC Scopus subject areas

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