Construction of automorphic Galois representations, II

By Gaëtan Chenevier, Michael Harris. 2013

130 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/db30803492682b134037c08c13d00ea9f1cfc3de

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In Geometry and Topology

1. T. Gee
2. Peter Scholze
3. J. Thorne
4. Ana Caraiani
5. M. Emerton
6. David Geraghty
7. F. Herzig
8. Richard Taylor

In Mathematical Physics

1. T. Gee
2. Peter Scholze
3. J. Thorne
4. Ana Caraiani
5. M. Emerton
6. David Geraghty
7. F. Herzig
8. Richard Taylor

Citations in the corpus

• A geometric perspective on the Breuil–Mézard conjecture (2011, result): “f Corollaire 5.3 of [Lab09], Theorem 1.1 of [BLGGT12], and Theorem 4.1.5. (Note that the purity assumption in Theorem 4.1.5 holds by Theorem 1.2 of [Car12], which builds on the results of [Shi11] and [CH11].) We note that our assumptions on v 1 imply that Sλ,τ(U,O)m⊗Zp Qpis free over TT λ,τ(U,O)m[1/”
• On the p-adic cohomology of the Lubin-Tate tower (2015, unknown): “Thus, this provides an alternative argument for Taylor’s construction of these Galois representations, [34], and it seems reasonable to expect that one could do a similar argument in the compact unitary case, providing an alternative to the construction of Galois representations of Shin, [32], and C”
• On the rigid cohomology of certain Shimura varieties (2014, methodology): “[CH] G. Chenevier and M. Harris, Construction of automorphic Galois representations II, to appear Cambridge Math.”
• Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “combine Shin’s earlier work [96, Th. 1.2] with Labesse’s restricted base change [64]. In particular our results use neither Shin’s extended base change [97, Th. A.1], nor the work of Chenevier-Harris [22]. 12 11. Systems of Hecke eigenvalues on the generalized superpecial locus This section is conce”
• WHITTAKER PERIODS, MOTIVIC PERIODS, AND SPECIAL VALUES OF TENSOR PRODUCT $L$ -FUNCTIONS (2013, background): “K) × GL1(AK), is expected to bear the following relation to the desired M(Π): (4.21) M′(πs,Vs;r) ∼= ∧r(M(Π)∨) ⊗M(ξc) This is known to be true in most cases at the level of Galois representations (cf. [7], Proposition 4.3.8, as well as the more complete results of Shin and Scholze–Shin), but in the a”
• Serre weights for rank two unitary groups (2011, unknown): “τ,1 +1,λıτ,2}. (3) If v∤lthen ıWD(rl,ı(π)|GF v )F−ss ∼= rec(π∨ v ⊗|det| −1/2). (4) If v|lthen ıWD(rl,ı(π)|GF v )ss ∼= rec(π∨ v ⊗|det| −1/2)ss. Proof. This follows immediately from the main results of [CH09], [Car10] and [BLGGT11]. After conjugating, we may assume that rl,ı(π) takes values in GL2(OQ ”