Number Theory Seminar

Speaker: Hui Gao (Helsinki)

Title: Overconvergence of etale $(\phi,\tau)$-modules.

Abstract: The category of etale $(\varphi, \tau)$-modules, similar as the category of etale $(\varphi, \Gamma)$-modules, is equivalent to the category of p-adic Galois representations. A classical theorem of Cherbonnier-Colmez says that all etale $(\varphi, \Gamma)$-modules are overconvergent. In this talk, we show that all etale $(\varphi, \tau)$-modules are also overconvergent. Our method is completely different from that of Cherbonnier-Colmez. The key idea is a certain crystalline approximation technique. This is joint work with Tong Liu.

More information:
https://www.math.ku.dk/english/research/tfa/alg/ntseminar/ 
http://www.n-cube.net/