p-Adic Automorphic Forms on Shimura Varieties

By H. Hida. 2004

215 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b5ba9a32d40476a3171db2cb2dcced29d9829f8e

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In Discrete Mathematics and Combinatorics

1. T. Gee
2. J. Thorne
3. Richard Taylor
4. C. Skinner
5. Michael Harris
6. V. Pilloni
7. Chao Zhang
8. Frank Calegari

In Geometry and Topology

1. T. Gee
2. J. Thorne
3. Frank Calegari
4. David Geraghty
5. Richard Taylor
6. Peter Scholze
7. Michael Harris
8. Ana Caraiani

In Mathematical Physics

1. T. Gee
2. J. Thorne
3. Frank Calegari
4. David Geraghty
5. Richard Taylor
6. Peter Scholze
7. Michael Harris
8. Ana Caraiani

Citations in the corpus

• Abelian surfaces over totally real fields are potentially modular (2018, methodology): “The classical Hida theory is developed in [Hid04] and takes the form of a projective module over the total weight space (which is 2[F : Q]-dimensional).”
• On the rigid cohomology of certain Shimura varieties (2014, background): “In many cases such a theorem has been proved by Hida in [Hi], but not in the full generality in which we are working here.)”
• The Iwasawa Main Conjectures for GL2 (2014, methodology): “This theory is nowadays well understood (see [Hi99],[Hi04],[Ur04]), but since there is no complete reference for the case we need, we give an account, sketching proofs, of what is necessary for our purposes.”
• Ekedahl-Oort Strata for Good Reductions of Shimura Varieties of Hodge Type (2013, background): “Let E be the reflex field of the PEL-Shimura datum D , note that the conditions on D implie that E/Q is unramified at p (see [18] page 306, the second paragraph from the bottom, or our proof of Proposition 2.”
• Galois representations modulo p and cohomology of Hilbert modular varieties (2004, unknown): “We denote by Ω±f ∈ C×/O× any two complementary periods defined by the Eichler-Shimura-Harder isomorphism (see §4.2).”
• THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS (2015, unknown): “v∈Σ z−1 v ; • θ|A×F = | · |FχK/F ; • Nm(fθ) = (M θ ) for some Mθ ∈ F× prime to p and such that DKM |Mθ and v|Mθ for all v ∈ Σ \ {p}; • for some v|D̃K, the anticyclotomic part of θ|OK,q has order divisible by qv; • Ω−2Σ ∞ L(1, θ) is a p-adic unit, where Ω∞ is the CM period defined in [15]; • θv,2(p)−”