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Improvements on Dieulefait-Manoharmayum and applications

Research paper by Luis V. Dieulefait

Indexed on: 10 Aug '05Published on: 10 Aug '05Published in: Mathematics - Number Theory



Abstract

We improve the results in a previous article of Dieulefait and Manoharmayum and we deduce some stronger modularity results. In particular we deduce that any rigid Calabi-Yau threefold defined over Q with good reduction at 5 is modular and we also obtain a fairly general version of the principle of "switching the residual characteristic" used in proofs of cases of Serre's conjecture.