The University of Arizona

Residual irreducibility of compatible systems

Residual irreducibility of compatible systems

Series: Algebra and Number Theory Seminar
Location: ENR 2 S395
Presenter: Stefan Patrikis, University of Utah

We show that a compatible system of absolutely irreducible l-adic representations of the Galois group of a number field is, for a density one set of l, also absolutely irreducible modulo l. The theorem generalizes previous work of Barnet-Lamb, Gee, Geraghty, and Taylor (for Hodge-Tate regular Galois representations) and of Zarhin (for Tate modules of abelian varieties). This is joint work with Andrew Snowden and Andrew Wiles.

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