Time：13:00-17:00, Thursday, January 16 2025
Venue：E4-233
Speaker：Hansheng Diao, YMSC/Tsinghua
Title：Monodromy and rigidity of crystalline local systems
Abstract：We study certain rigidity properties of p-adic local systems on a smooth scheme X over a p-adic field. In particular, we show that the monodromy of the log (iso)crystal attached to a semistable local system is rigid along irreducible components of the special fiber. There are several applications. Firstly, suppose that X has good reduction. We show that, if a family of semistable representations is crystalline at one classical point on X, then it is crystalline everywhere. Secondly, for any p-adic local system on a smooth projective curve with good reduction, if it is potentially crystalline at one classical point, then it is potentially crystalline everywhere. Finally, we show that a p-adic local system over the punctured disc extends to a (necessarily crystalline) p-adic local system over the entire disc if it is crystalline at all classical points. In other words, such a local system cannot have geometric monodromy if it has no arithmetic monodromy everywhere on the punctured disc. This is a joint work with Zijian Yao.
