Arithmetic Geometry and Number Theory RTG Seminar: Finiteness of Frobenius traces of a de Rham local system

Seminar | October 1 | 3:10-5 p.m. | 784 Evans Hall

 Koji Shimizu, UC Berkeley

 Department of Mathematics

Pre-talk: For a Galois representation of a number field arising from a smooth projective variety, the Weil conjecture tells that its Frobenius traces are rational numbers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property of Frobenius traces. In the pretalk, I will explain these backgrounds.

Main talk: Etale local systems on an algebraic variety are a natural generalization of Galois representations of a filed. In the main talk, I will focus on de Rham local systems and explain a finiteness result on Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis.