The Geometry and Cohomology of Some Simple Shimura Varieties.

By Michael Harris, Richard Taylor, V. Berkovich. 2002

1,120 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eadcc16fe2aba10245f4d94a12191d333e393fa4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. T. Gee
2. Peter Scholze
3. M. Emerton
4. J. Thorne
5. David Geraghty
6. Ana Caraiani
7. W. Gan
8. Frank Calegari

In Mathematical Physics

1. Peter Scholze
2. T. Gee
3. J. Thorne
4. M. Emerton
5. David Geraghty
6. Akshay Venkatesh
7. W. Gan
8. Frank Calegari

Citations in the corpus

• Functoriality for the quasisplit classical groups (2011, neutral): “By composing with ιv : Gn ↪→ HN we have an unramified admissible homomorphism Φv = ιv◦φv :Wkv −→ HN and this defines an irreducible admissible unramified representation Πv of HN (kv) [17, 18].”
• Irreducibility of automorphic Galois representations of GL(n), n at most 5 (2011, methodology): “In [27], this observation was used to prove the irreducibility of the Galois representations considered in [17] whenever the square-integrability hypothesis holds.”
• Functoriality for the classical groups (2004, methodology): “By composing with ι : Gn(C) ↪→ GLN(C) we have an unramified admissible homomorphism Φv = ι ◦ φv : Wkv −→ GLN(C) and this defines an irreducible admissible representation Πv of GLN(kv) [15,17].”
• The emerging p-adic Langlands programme (2011, methodology): “If F is a field which is a finite extension of Qp and n a positive integer, the celebrated local Langlands programme for GLn ([48], [37], [38]) establishes a “natural” 1 − 1 correspondence between certain Q`-linear continuous representations ρ of the Galois group Gal(Qp/F ) on n-dimensional Q`-vecto”
• Generalized Whittaker models and the Bernstein center (2003, background): “To show that the wildly ramified correspondence of [7] is the same as the Langlands correspondence of [13], [14], one has to verify some delicate arithmetic properties of the local constant of certain pairs of representations [8].”
• Families of L -Functions and Their Symmetry (2014, background): “transport of the modulus character on K × via class field theory. The local Langlands reciprocity map is a bijection recK : Rep(GLn(K))C → Repn(WK)C uniquely characterized by a list of properties, cf. [53]. In particular L(s,π) = L(s,rec(π)), ε(s,π,ψ) = ε(rec(π),ψ)foranynontrivial additive character ”
• On torsion in the cohomology of locally symmetric varieties (2013, methodology): “We combine this theorem with the existence of Galois representation ([23], [45], [37], [57], [21]; the precise statement we need is stated as [10, Theorems 1.”
• Riemann's zeta function and beyond (2003, positive): “Now, thanks to the recent proof of the local Langlands correspondence by Harris and Taylor for GL(n) [14], [57], [59], [62], [63], [65], [101], the definitions at the ramified places can be made also.”
• Formal degrees and local theta correspondence (2013, positive): “Moreover, it follows from a result of Henniart [33] that γ Sh(2s, τ,R,ψ)= α · γ (2s,R ◦ φτ ,ψ) with some root of unity α, where φτ is the L-parameter associated to τ by the local Langlands correspondence [27, 32].”
• COMPANION FORMS FOR UNITARY AND SYMPLECTIC GROUPS (2010, methodology): “spectively globally generic). Finally, we say in addition that ρis automorphic of level prime to lif πl is unramified. In recent work ([Sor08]) Sorensen has used Theorem 7.6.1 and the constructions of [HT01] to associate Galois representations to certain globally generic cuspidal representations of G”