Even Galois Representations and the Cohomology Of GL(2,Z)
Even Galois Representations and the Cohomology Of GL(2,Z)

Avner Ash , Boston College
Fine Hall 214
Let F be a field of characteristic not equal to 2. Let r be a 2dimensional even Galois representation which is induced from an Fvalued character of odd order of the absolute Galois group of a real quadratic field K. After imposing some additional conditions on the inducing character c, we attach r to a Hecke eigenclass in the cohomology of GL(2,Z) with coefficients in a certain countablyinfinitedimensional vector space over F. We hope that this work will enable us to prove some cases of a Serretype conjecture for certain reducible 3dimensional Galois representations. This is joint work with Darrin Doud.