On Langlands functoriality- reduction to the semistable case

TL;DR

This paper extends a method for establishing Langlands functoriality by reducing the problem to the semistable case, leveraging cyclic base change and descent to simplify proofs of the correspondence.

Contribution

It generalizes a technique to prove Langlands functoriality by focusing on the semistable case under cyclic base change and descent assumptions.

Findings

Reduction of Langlands functoriality to semistable case.

Applicability of cyclic base change and descent in the proof.

Simplification of demonstrating the correspondence.

Abstract

We generalize a beautiful method of Blasius and Ramakrishnan, that in order to exhibit particular instances of the Langlands functorial correspondence, it is enough to show that the correspondence holds in the semistable case, provided the arithmetic data we are considering is closed with respect to cyclic base change and descent.