Arithmetic Compactifications of PEL-Type Shimura Varieties

By Kai-Wen Lan. 2013

225 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3bdd37bdb2df0746acb71664518764ccfb5bf2fa

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In Geometry and Topology

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Citations in the corpus

On the rigid cohomology of certain Shimura varieties (2014, methodology): “5 of [41]) is just Q, and S0 = Spec F0 = SpecQ.”
Iwasawa Main Conjecture for Supersingular Elliptic Curves (2014, background): “For the theory of compactifications of SG(K), see [42].”
Eisenstein congruence on unitary groups and Iwasawa main conjectures for CM fields (2014, methodology): “7.2.3.11 [Lan08]).”
Comparison between analytic and algebraic constructions of toroidal compactifications of PEL-type Shimura varieties (2011, background): “Let us explain how to carry out the corrections (compatible with the corrections made to [1] and in [2] in their errata) and the necessary improvements for the exposition: (a) In Def.”
THE IWASAWA MAIN CONJECTURE FOR HILBERT MODULAR FORMS (2015, unknown): “such that the components of K are GL4(Zp) at all primes above p and the automorphic sheaves ωk and the universal differential sheaf ω to [28], [15] and [20] respectively.”
Strata Hasse invariants, Hecke algebras and Galois representations (2015, methodology): “In-between the works of Chai-Faltings and Madapusi-Pera, generalizations to the intermediate PEL case were given in a series of works by Lan [66, 65, 71, 72].”
Cycles on Shimura varieties via geometric Satake (2017, background): “On the other hand, the Hecke algebra Cc(G(Zp)\G(Qp)/G(Zp)) naturally acts on Hc(Shµ,k̄v): the existence of smooth toroidal compactification ([Lan13] [MP15]) implies that after choosing a specialization map k̄v → Ēv, there is an isomorphism Hc(Shµ,k̄v) ' Hc(ShK(G,X)Ēv), and since the action of the…”
Toroidal compactifications of integral models of Shimura varieties of Hodge type (2012, methodology): “Using [Lan08, 6.4.1.1(6)], one can now show that there exists a complete local ring R′ at the boundary of a smooth toroidal compactification of an appropriate moduli space of polarized abelian varieties, equipped with a ‘universal’ tuple (B′, λab, ′ , Y,X, λét, c′, c∨, ′ , τ ′), and a map R′ → R…”
On the generic part of the cohomology of non-compact unitary Shimura varieties (2019, methodology): “See [Lan13, Definition 5.4.2.6] and [LS18a, Remark 4.3.3] for an explanation of why the description of the boundary stratum simplifies in our case, when the level K = K(N) is principal, when p -”
Abelian surfaces over totally real fields are potentially modular (2018, unknown): “For convenience, our main references for integral models of PEL Shimura varieties and their compactifications are the papers [Lan13, Lan16, Lan17], although some of the results we cite from there were proved in earlier papers, in particular [Kot92]; we refer the reader to the references in [Lan13]…”