Geodesic
Potential automorphy and change of weight
Thomas Barnet-Lamb1 ; Toby Gee2 ; David Geraghty3 ; Richard Taylor4
1 Brandeis University, Waltham, MA
2 Imperial College London, London, UK
3 Boston College, Chestnut Hill, MA
4 Institute for Advanced Study, Princeton, NJ
Annals of mathematics, Tome 179 (2014) no. 2, pp. 501-609.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove an automorphy lifting theorem for $l$-adic representations where we impose a new condition at $l$, which we call “potentential diagonalizability.” This result allows for “change of weight” and seems to be substantially more flexible than previous theorems along the same lines. We derive several applications. For instance we show that any irreducible, totally odd, essentially self-dual, regular, weakly compatible system of $l$-adic representations of the absolute Galois group of a totally real field is potentially automorphic and hence is pure and its $L$-function has meromorphic continuation to the whole complex plane and satisfies the expected functional equation.
DOI : 10.4007/annals.2014.179.2.3

Thomas Barnet-Lamb 1 ; Toby Gee 2 ; David Geraghty 3 ; Richard Taylor 4

1 Brandeis University, Waltham, MA
2 Imperial College London, London, UK
3 Boston College, Chestnut Hill, MA
4 Institute for Advanced Study, Princeton, NJ 
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Thomas Barnet-Lamb; Toby Gee; David Geraghty; Richard Taylor. Potential automorphy and change of weight. Annals of mathematics, Tome 179 (2014) no. 2, pp. 501-609. doi : 10.4007/annals.2014.179.2.3. http://geodesic.mathdoc.fr/articles/10.4007/annals.2014.179.2.3/

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