@article{781ee4dbe57f4ee0b5999ab6d8185330,
title = "The Galois action and cohomology of a relative homology group of Fermat curves",
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.",
keywords = "Cohomology, Cyclotomic field, Fermat curve, Galois module, Hochschild–Serre spectral sequence, Homology, Resolution, {\'E}tale fundamental group",
author = "Rachel Davis and Rachel Pries and Vesna Stojanoska and Kirsten Wickelgren",
note = "Funding Information: We would like to thank BIRS for hosting the WIN3 conference where we began this project and AIM for support for this project through a Square collaboration grant. We would like to thank a referee for helpful comments. Some of this work was done while the third and fourth authors were in residence at MSRI during the spring 2014 Algebraic topology semester, supported by NSF grant 0932078 000. The second author was supported by NSF grant DMS-15-02227. The third author was supported by NSF grants DMS-1606479 and DMS-1307390. The fourth author was supported by an American Institute of Mathematics five year fellowship and NSF grants DMS-1406380 and DMS-1552730. Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",
year = "2018",
month = jul,
day = "1",
doi = "10.1016/j.jalgebra.2018.02.021",
language = "English (US)",
volume = "505",
pages = "33--69",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}