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

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 associat...

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Bibliographic Details
Published inJournal of algebra Vol. 505; pp. 33 - 69
Main Authors Davis, Rachel, Pries, Rachel, Stojanoska, Vesna, Wickelgren, Kirsten
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2018
Subjects
Cohomology
Cyclotomic field
Fermat curve
Galois module
Hochschild–Serre spectral sequence
Homology
Resolution
Étale fundamental group
Galois module
11D41
Cyclotomic field
Homology
Cohomology
14F35
11R18
13A50
55S35
Fermat curve
Étale fundamental group
55T10
11R34
Hochschild–Serre spectral sequence
Resolution
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Summary: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.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2018.02.021