On the rigid cohomology of certain Shimura varieties
By Michael Harris, Kai-Wen Lan, Richard Taylor, J. Thorne. 2014
129 citations recorded by the source corpus.
We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of $$GL_n$$GLn over a CM (or totally real) field and check local–global compatibility for the l-adic representation away from l and a finite number of rational primes above which the CM field or the automorphic representation ramifies. The main innovation is that we impose no self-duality hypothesis on the automorphic representation.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8dd7f0fe85484962f8b860357ac8d6945d05ce01
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In Geometry and Topology
- Akshay Venkatesh
- Peter Scholze
- Frank Calegari
- W. Goldring
- Jean-Stefan Koskivirta
- David Geraghty
- T. Gee
- Kiran S. Kedlaya
In Mathematical Physics
- Akshay Venkatesh
- Peter Scholze
- Frank Calegari
- W. Goldring
- Jean-Stefan Koskivirta
- David Geraghty
- T. Gee
- Kiran S. Kedlaya
Citations in the corpus
- p-ADIC GEOMETRY (2017, methodology): “e exists a corresponding continuous semisimple Galois representation ˆ ˇ: Gal(F=F) ! GL n(Q ‘) unramied at good primes. The nal part of this theorem was proved previously by Harris-Lan-TaylorThorne, [HLTT16]. The general strategy is to realize X K as a boundary component of the Borel-Serre compactic”
- Modularity lifting beyond the Taylor–Wiles method (2012, methodology): “In particular, our methods require Galois representations associated to torsion classes which do not necessarily lift to characteristic zero, where one might hope to apply the recent results of [7].”
- A torsion Jacquet--Langlands correspondence (2012, background): “Scholze’s argument is thus by necessity somewhat more subtle, and we direct the reader to [84] for details (we should also point out the recent paper [45] which proves a related theorem in characteristic zero).”
- Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “Moreover, the argument we use is analogous to the one introduced by Taylor [101], and then applied in [54, 32, 39, 50].”