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

Rachel Davis, Rachel Pries, Vesna Stojanoska, Kirsten Wickelgren

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)33-69
Number of pages37
JournalJournal of Algebra
Volume505
DOIs
StatePublished - 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

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