Reconstruction of function fields

Fedor Bogomolov; Yuri Tschinkel

doi:10.1007/s00039-008-0665-8

Reconstruction of function fields

Fedor Bogomolov, Yuri Tschinkel

Mathematics

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

Abstract

For k an algebraic closure of the finite field double-struck F sign p ,ℓ prime distinct from p and X a surface over k, we prove that the field of rational functions k(X) can be recovered from the maximal pro-ℓ-quotient GK of its absolute Galois group - in fact already from the second central descending series quotient of GK .

Original language	English (US)
Pages (from-to)	400-462
Number of pages	63
Journal	Geometric and Functional Analysis
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/s00039-008-0665-8
State	Published - Jul 2008

Keywords

Function fields
Galois groups

ASJC Scopus subject areas

Analysis
Geometry and Topology

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title = "Reconstruction of function fields",

abstract = "For k an algebraic closure of the finite field double-struck F sign p ,ℓ prime distinct from p and X a surface over k, we prove that the field of rational functions k(X) can be recovered from the maximal pro-ℓ-quotient GK of its absolute Galois group - in fact already from the second central descending series quotient of GK .",

keywords = "Function fields, Galois groups",

author = "Fedor Bogomolov and Yuri Tschinkel",

note = "Funding Information: Acknowledgments. Both authors were partially supported by the NSF. The second author was employed by the Clay Mathematics Institute. We are grateful to Laurent Lafforgue and Barry Mazur for their interest and the referee for many useful remarks. Comments by Pierre Deligne were of tremendous help.",

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journal = "Geometric and Functional Analysis",

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AU - Tschinkel, Yuri

N1 - Funding Information: Acknowledgments. Both authors were partially supported by the NSF. The second author was employed by the Clay Mathematics Institute. We are grateful to Laurent Lafforgue and Barry Mazur for their interest and the referee for many useful remarks. Comments by Pierre Deligne were of tremendous help.

PY - 2008/7

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N2 - For k an algebraic closure of the finite field double-struck F sign p ,ℓ prime distinct from p and X a surface over k, we prove that the field of rational functions k(X) can be recovered from the maximal pro-ℓ-quotient GK of its absolute Galois group - in fact already from the second central descending series quotient of GK .

AB - For k an algebraic closure of the finite field double-struck F sign p ,ℓ prime distinct from p and X a surface over k, we prove that the field of rational functions k(X) can be recovered from the maximal pro-ℓ-quotient GK of its absolute Galois group - in fact already from the second central descending series quotient of GK .

KW - Function fields

KW - Galois groups

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SN - 1016-443X

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