The Galois action and cohomology of a relative homology group of Fermat curves

Rachel Davis; Rachel Pries; Vesna Stojanoska; Kirsten Wickelgren

doi:10.1016/j.jalgebra.2018.02.021

The Galois action and cohomology of a relative homology group of Fermat curves

Rachel Davis, Rachel Pries, Vesna Stojanoska, Kirsten Wickelgren

Mathematics

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

Abstract

For an odd prime p satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group G_{Q(ζ_p)} on the homology of the degree p Fermat curve, building on work of Anderson. Further, we study the invariants and the first Galois cohomology group which are associated with obstructions to rational points on the Fermat curve.

Original language	English (US)
Pages (from-to)	33-69
Number of pages	37
Journal	Journal of Algebra
Volume	505
DOIs	https://doi.org/10.1016/j.jalgebra.2018.02.021
State	Published - Jul 1 2018

Keywords

Cohomology
Cyclotomic field
Fermat curve
Galois module
Hochschild–Serre spectral sequence
Homology
Resolution
Étale fundamental group

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1016/j.jalgebra.2018.02.021

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abstract = "For an odd prime p satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group GQ(ζp) on the homology of the degree p Fermat curve, building on work of Anderson. Further, we study the invariants and the first Galois cohomology group which are associated with obstructions to rational points on the Fermat curve.",

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AU - Davis, Rachel

AU - Pries, Rachel

AU - Stojanoska, Vesna

AU - Wickelgren, Kirsten

PY - 2018/7/1

Y1 - 2018/7/1

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AB - For an odd prime p satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group GQ(ζp) on the homology of the degree p Fermat curve, building on work of Anderson. Further, we study the invariants and the first Galois cohomology group which are associated with obstructions to rational points on the Fermat curve.

KW - Cohomology

KW - Cyclotomic field

KW - Fermat curve

KW - Galois module

KW - Hochschild–Serre spectral sequence

KW - Homology

KW - Resolution

KW - Étale fundamental group

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SN - 0021-8693

VL - 505

SP - 33

EP - 69

JO - Journal of Algebra

JF - Journal of Algebra

ER -

The Galois action and cohomology of a relative homology group of Fermat curves

Abstract

Keywords

ASJC Scopus subject areas

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