The infinite base change lifting associated to an APF extension of a $p$-adic field (Algebraic Number Theory and Related Topics 2015)

Abstract

In this paper, we construct a base change lifting for an APF extension of a mixed characteristic local field. We do this by combining Arthur - Clozel's base change lifting with an operation coming from Kazhdan's theory of close local fields and Fontaine - Wintenberger's theory of fields of norms. Key facts are: (1) a compatibility of Deligne's and Kazhdan's theories of close local fields via the local Langlands correspondence, and (2) a coincidence of the restriction of the Galois groups with respect to a totally ramified extension and an operation coming from Deligne's theory.