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 AHGT Video Series

p-adic L-function survey + epsilon - T.Ochiai

Sep 2, 2024  ·   In Kyoto Japan  ·   Event ``AHGT Seminar''

Abstract

To a given motive or a Galois representation over a number field, we can associate a Hasse-Weil L-function, which is conjecturally a meromorphic function defined over the whole complex plane. According to the Langlands conjecture this Hasse-Weil L-function corresponds to the automorphic L-function of the corresponding automorphic representation.
If we take a prime number p, which is an ordinary prime of this motive, we can consider the p-adic counterpart of this Hasse-Weil L-function, which is called the p-adic L-function. The existence of such a p-adic L-function is conjectural, but for motives of lower ranks the construction is known. In this talk, we can not give an updated overview of the known cases and recent works, but we recall the classical conjecture of the existence (mainly due to Coates and Perrin-Riou) and we explain what we have to check to construct the p-adic L-function.
If time permits, we want to discuss a very short overview of future perspectives on the p-adic L-function associated with (a p-adic deformation of) a motive.


 Program & participants
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License 2025 · Creator: AHGT IRN Group  · Impressum · Last updated: May 06, 2025 from Kyoto Japan  · 
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