# Mathematics Colloquia and Seminars

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### Arithmetic representations of fundamental groups

**Algebraic Geometry**

Speaker: | Daniel Litt, Columbia University |

Related Webpage: | https://www.daniellitt.com |

Location: | 2112 MSB |

Start time: | Wed, Nov 29 2017, 11:00AM |

Let X be an algebraic variety over a field k. Which representations of pi_1(X) arise from geometry, e.g. as monodromy representations on the cohomology of a family of varieties over X? We study this question by analyzing the action of the Galois group of k on the fundamental group of X, and prove several fundamental structural results about this action.

As a sample application of our techniques, we show that if X is a normal variety over a field of characteristic zero, and p is a prime, then there exists an integer N=N(X,p) such that any non-trivial p-adic representation of the fundamental group of X, which arises from geometry, is non-trivial mod p^N.