The infinite base change lifting associated to an APF extension of a $p$-adic field

TL;DR

This paper establishes a connection between base change liftings for totally ramified extensions of non-archimedean local fields and Kazhdan's close fields theory, enabling new liftings for APF extensions.

Contribution

It demonstrates that base change liftings align with close fields theory under certain conditions and extends this to APF extensions of mixed characteristic local fields.

Findings

Base change lifting coincides with close fields theory for certain extensions.

Construction of base change lifting for APF extensions.

Extension of lifting theory to mixed characteristic local fields.

Abstract

In this paper, the author proved that the base change lifting associated to a totally ramified extension of a non-archimedean local field coincides with a map coming from the close fields theory of Kazhdan under some conditions. As a corollary, we can construct a base change lifting for an APF extension of a mixed characteristic local field.