On the Meromorphic Continuation of Degree Two L-Functions

By Richard Taylor. 2006

128 citations recorded by the source corpus.

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Citations in the corpus

Automorphic lifts of prescribed types (2008, result): “ve some of results used in [Gee08], and to discuss some related conjectures. We assume that p>2. We begin by recalling some standard facts from the theory of quaternionic modular forms; see either [Tay06], section 3 of [Kis07b] or section 2 of [Kis09a] for more details, and in particular the proo”
On the weights of mod p Hilbert modular forms (2006, methodology): “We begin by recalling some standard facts from the theory of quaternionic modular forms; see either [ Tay06 ], section 3 of [Kis08a] or section 2 of [Kis08b] for more details, and in particular the proofs of the results claimed below.”
A Family of Calabi–Yau Varieties and Potential Automorphy II (2011, unknown): “To generalise the results of [T1] and [ T2 ] to higher dimensional representations two things were needed: generalisations of the ‘modularity of lifts’ theorems of Wiles [W] and Taylor-Wiles [TW] from GL2 to GSpn (or some similar group); and families of ‘motives’ with large monodromy but with hi,j ≤”
On the p-adic cohomology of the Lubin-Tate tower (2015, methodology): “To apply the Taylor-Wiles patching technique [36], adapted to the case of totally real fields in [35], we impose some usual hypothesis, cf.”
Congruences between Hilbert modular forms: constructing ordinary lifts (2010, background): “,ψ(Ul,O) ⊗O,ιC −→∼ M Π HomO× B,l (W∨ τ,C,Πl) ⊗Π ∞,l where the sum is over all automorphic representations Π of (B⊗QA)× of weight 0 and central character ψC (see for instance the proof of Lemma 1.3 of [Tay06]). Let U be as above and let Rdenote a ﬁnite set of places of F+ 1 containing all those place”
The Sato-Tate conjecture for Hilbert modular forms (2009, unknown): “C,Πl) ⊗Π ∞,l where the sum is over all automorphic representations Π of (B⊗Q A)× of weight ι∗λ′ := (λ′ ι−1σ)σ ∈(Z 2 +) Hom(F′,C) and central character ψ′ C (see for instance the proof of Lemma 1.3 of [Tay06]). 50 THOMAS BARNET-LAMB, TOBY GEE, AND DAVID GERAGHTY Let U be as above and let Rdenote a ﬁn”
Serre’s modularity conjecture (II) (2009, methodology): “When ρ̄|D2 is irreducible ([51]), the polarization data j is an isomorphism (δ−1 M ) ' P(A, i).”