时间：2024年6月5日（星期三）14:00-16:00
地点：西湖大学云谷校区E4-201
主讲人：段炼，上海科技大学
报告题目：On the irreducibility of low-dimensional geometric Galois representations
报告摘要：In this talk, we discuss the irreducibility of compatible systems of certain five-dimensional geometric Galois representations. Using the modularity results of classical cases, we prove that such a compatible system of representations is either irreducible for almost all p, or decompose uniformly as p varies. Our irreducibility result will deduce an algorithm for checking the irreducibility of corresponding Galois representations. Moreover, by applying a result of Cadoret and Tamagawa on the open image theory of monodromy representation, we can spread out the irreducibility among the family of representations induced by the transcendental part of a family of elliptic surfaces. If time allows, I will talk about a concrete example as application of our main result.
