Congruences betwen Hilbert modular forms: constructing ordinary lifts II

TL;DR

This paper improves previous results by proving a near-optimal theorem on the existence of ordinary lifts of mod l Hilbert modular forms for any odd prime l, advancing the understanding of modular form lifts.

Contribution

It provides a near-optimal theorem on the existence of ordinary lifts of mod l Hilbert modular forms for all odd primes l, refining earlier results.

Findings

Proves a near-optimal theorem on ordinary lifts.

Extends results to all odd primes l.

Enhances understanding of Hilbert modular form lifts.

Abstract

In this note we improve on the results of our earlier paper[BLGG12], proving a near-optimal theorem on the existence of ordinary lifts of a mod l Hilbert modular form for any odd prime l.