Ahmed Abbes (CNRS, IHÉS), Christophe Breuil (CNRS, Université Paris-Sud), Takeshi Saito - 斎藤　毅 (Université de Tokyo - 東大数理)
Atsushi Shiho - 志甫　淳 (Université de Tokyo - 東大数理), Takeshi Tsuji - 辻　雄 (Université de Tokyo - 東大数理)

T. Abe (IPMU, Tokyo)

Product formula for p-adic epsilon factors

In the 80's, Deligne conjectured that some constant appearing in the functional equation of the $L$-function of an l-adic lisse sheaf on a curve over a finite field can be written as product of local contributions, and proved some special cases.The conjecture was established later by Laumon, and was used by Lafforgue in his proof of the Langlands' conjecture for function fields. We prove a $p$-adic analogue of this product formula (joint work with A. Marmora).