Speaker: Prof. Anna Cadoret ，Sorbonne Université

Inviter: 郑维喆研究员

Title: Trivial locus of l-adic local system

Language: English

Time & Venue: 2024.04.18 15:00-16:00 MCM110

Abstract: We will discuss and provide evidence for the following consequence of the unramified Fontaine-Mazur conjecture. Let X be a variety over a number field and V a l-adic local system on X. If there exists a closed point x on X such that the pull-back x^*V is finite (viz the corresponding Galois rep has finite image) then V itself is finite. We obtain partial results, using a mix of (variational) p-adic Hodge theory and companions plus a "point-wise to global" principle for the properties of being unramified and tamely ramified. This is a joint work with Akio Tamagawa.