Results 21 to 30 of about 54 (54)

Canonical integral models for Shimura varieties of abelian type

Forum of Mathematics, Sigma
We prove a conjecture of Pappas and Rapoport for all Shimura varieties of abelian type with parahoric level structure when $p>2$ by showing that the Kisin–Pappas–Zhou integral models of Shimura varieties of abelian type are canonical.
Patrick Daniels, Alexander Youcis
doaj   +1 more source

Local-global compatibility for regular algebraic cuspidal automorphic representations when $\ell \neq p$

Forum of Mathematics, Sigma
We prove the compatibility of local and global Langlands correspondences for $\operatorname {GL}_n$ up to semisimplification for the Galois representations constructed by Harris-Lan-Taylor-Thorne [10] and Scholze [18]. More precisely, let $r_p(
Ila Varma
doaj   +1 more source

UNRAMIFIEDNESS OF GALOIS REPRESENTATIONS ARISING FROM HILBERT MODULAR SURFACES

Forum of Mathematics, Sigma, 2017
Let $p$ be a prime number and $F$ a totally real number ...
MATTHEW EMERTON, DAVIDE REDUZZI, LIANG XIAO   +2 more
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THE SHIMURA CURVE OF DISCRIMINANT 15 AND TOPOLOGICAL AUTOMORPHIC FORMS

Forum of Mathematics, Sigma, 2015
We find defining equations for the Shimura curve of discriminant 15 over $\mathbb{Z}[1/15]$. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher cohomology. We apply this to calculate the homotopy groups
TYLER LAWSON
doaj   +1 more source

Likely intersections

Forum of Mathematics, Sigma
We prove a general likely intersections theorem, a counterpart to the Zilber-Pink conjectures, under the assumption that the Ax-Schanuel property and some mild additional conditions are known to hold for a given category of complex quotient spaces ...
Sebastian Eterović, Thomas Scanlon
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Kodaira–Spencer isomorphisms and degeneracy maps on Iwahori-level Hilbert modular varieties: the saving trace

Forum of Mathematics, Sigma
We consider integral models of Hilbert modular varieties with Iwahori level structure at primes over p, first proving a Kodaira–Spencer isomorphism that gives a concise description of their dualizing sheaves. We then analyze fibres of the degeneracy maps
Fred Diamond
doaj   +1 more source

Arithmetic Transfer for inner forms of $GL_{2n}$

Forum of Mathematics, Sigma
We formulate Guo–Jacquet type fundamental lemma conjectures and arithmetic transfer conjectures for inner forms of $GL_{2n}$ . Our main results confirm these conjectures for division algebras of invariant $1/4$ and $3/4$ .
Qirui Li, Andreas Mihatsch
doaj   +1 more source

Deformation theory for prismatic G-displays

Forum of Mathematics, Sigma
For a smooth affine group scheme G over the ring of p-adic integers and a cocharacter $\mu $ of G, we develop the deformation theory for G- $\mu $ -displays over the prismatic site of Bhatt–Scholze, and discuss how our deformation theory can ...
Kazuhiro Ito
doaj   +1 more source

p-adic Borel extension for local Shimura varieties

Forum of Mathematics, Sigma
We show that the moduli spaces of Scholze’s p-adic shtukas with framing satisfy a p-adic rigid analytic version of Borel’s extension theorem. In particular, this holds for local Shimura varieties, for all local Shimura data $(G, [b],\{\mu ...
Abhishek Oswal, Georgios Pappas
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On two theorems for flat, affine group schemes over a discrete valuation ring

Open Mathematics, 2005
Vasiu Adrian
doaj   +1 more source