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

JOURNAL OF ALGEBRA

卷:505

Article

Davis, Rachel¹  Pries, Rachel²  Stojanoska, Vesna³  Wickelgren, Kirsten⁴ 

[1] Univ Wisconsin Madison, Madison, WI 53706 USA

[2] Colorado State Univ, Ft Collins, CO 80523 USA

[3] Univ Illinois, Urbana, IL 61801 USA

[4] Georgia Inst Technol, Atlanta, GA 30332 USA

关键词: Fermat curve;    Cyclotomic field;    Homology;    Cohomology;    Etale fundamental group;    Galois module;    Resolution;    Hochschild-Serre spectral sequence;   

DOI  :  10.1016/j.jalgebra.2018.02.021

来源: Elsevier

【 摘 要 】

For an odd prime p satisfying Vandiver's conjecture, we give explicit formulae for the action of the absolute Galois group G(Q()(sigma 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free