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.

### Galois Seminar

Friday, March 24, 2017 - 3:15pm

#### Rachel Pries

Colorado State University