Relating two conjectures in p-adic Hodge theory
报告人：Leo Poyeton (Bordeaux)
时间：2025-4-23 09:45 -11:30
地点：王选报告厅
Abstract:
Lately, interest has risen around a generalization of the theory of $(\varphi,\Gamma)$-modules, replacing the cyclotomic extension with an arbitrary infinitely ramified $p$-adic Lie extension. Computations from Berger suggest that taking locally analytic vectors in some rings of periods should provide such a generalization for any arbitrary infinitely ramified $p$-adic Lie extension, and this has been conjectured by Kedlaya.
In this talk, I will compute those locally analytic vectors in the particular case of $\mathbf{Z}_p$-extensions. Using this result, I will construct, in the anticyclotomic setting and assuming that Kedlaya's conjecture holds, an element in the field of fractions of the Robba ring which ``should not exist'' according to a conjecture of Berger on substitution maps on the Robba ring.
