Factorization of Algebraic $p$-adic $L$-functions Attached to Adjoint Representations of Coleman Families: Non-critical Case

TL;DR

This paper proves a factorization formula for algebraic $p$-adic $L$-functions associated with adjoint representations of Coleman families, extending previous results to the non-ordinary case using advanced algebraic and geometric tools.

Contribution

It establishes the $p$-adic Artin formalism for these $L$-functions in the non-critical, non-ordinary setting, broadening the scope of earlier work.

Findings

Proves a factorization formula involving Selmer complexes.

Extends $p$-adic Artin formalism to non-ordinary cases.

Uses tools from rigid geometry, homological algebra, and $p$-adic Hodge theory.

Abstract

The main objective of this article is to establish the $p$-adic Artin formalism for the algebraic $p$-adic $L$-functions attached to the adjoint representations of Coleman families of modular forms. In particular, we prove a factorization formula involving the determinants of appropriate Selmer complexes, using tools from rigid geometry, homological algebra, Euler systems, and $p$-adic Hodge theory. This work extends an earlier result of Palvannan to the $p$-non-ordinary setting.