From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefolds
| dc.creator | Dieulefait, Luis | |
| dc.date | 2004-09-07 | |
| dc.date.accessioned | 2026-07-07T05:11:52Z | |
| dc.date.available | 2026-07-07T05:11:52Z | |
| dc.description | We prove modularity for any irreducible crystalline $\ell$-adic odd 2-dimensional Galois representation (with finite ramification set) unramified at 3 verifying an "ordinarity at 3" easy to check condition, with Hodge-Tate weights $\{0, w \}$ such that $2 w < \ell$ (and $\ell > 3$) and such that the traces $a_p$ of the images of Frobenii verify $\Q(\{a_p \}) = \Q $. This result applies in particular to any motivic compatible family of odd two-dimensional Galois representations of $\Gal(\bar{\Q}/\Q)$ if the motive has rational coefficients, good reduction at 3, and the "ordinarity at 3" condition is satisfied. As a corollary, this proves that all rigid Calabi-Yau threefolds defined over $\Q$ having good reduction at 3 and satisfying $ 3 \nmid a_3$ are modular. | |
| dc.identifier | https://arxiv.org/abs/math/0409102 | |
| dc.identifier | http://arxiv.org/abs/math/0409102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72391 | |
| dc.subject | Number Theory | |
| dc.title | From potential modularity to modularity for integral Galois representations and rigid Calabi-Yau threefolds | |
| dc.type | text |