Galois action on homology of Fermat curves

Algebra Seminar
Monday, January 9, 2017 - 3:05pm for 1 hour (actually 50 minutes)
Sklles 005
Rachel Pries – Colorado State University – pries@math.colostate.edu
Douglas Ulmer
We prove a result about the Galois module structure of the Fermat curve using commutative algebra, number theory, and algebraic topology. Specifically, we extend work of Anderson about the action of the absolute Galois group of a cyclotomic field on a relative homology group of the Fermat curve. By finding explicit formulae for this action, we determine the maps between several Galois cohomology groups which arise in connection with obstructions for rational points on the generalized Jacobian. Heisenberg extensions play a key role in the result. This is joint work with R. Davis, V. Stojanoska, and K. Wickelgren.