The Galois action and cohomology of a relative homology group of Fermat\n Curves

2016/10/06 by Rachel Davis, Davis, Rachel, Rachel Pries +5
Mathematics · Medicine · #11D41 #11R18 #11R34 #14F35 #14G25 #55S35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Leprosy Research and Treatment #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1610.02006

openalex publication_date 2016/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an odd prime p satisfying Vandiver's conjecture, we give explicit\nformulae for the action of the absolute Galois group G_\ℚ(\ζp)\non the homology of the degree p Fermat curve, building on work of Anderson.\nFurther, we study the invariants and the first Galois cohomology group which\nare associated with obstructions to rational points on the Fermat curve.\n

Related

• Galois action on the homology of Fermat curves
• Galois action on homology of generalized Fermat Curves
• Cohomology groups of Fermat curves via ray class fields of cyclotomic\n fields
• The Galois action on the lower central series of the fundamental group of the Fermat curve
• Galois Action on Homology of the Heisenberg Curve