Results 11 to 20 of about 44 (44)

Mod p points on shimura varieties of parahoric level

Forum of Mathematics, Pi
We study the $\overline {\mathbb {F}}_{p}$ -points of the Kisin–Pappas integral models of Shimura varieties of Hodge type with parahoric level. We show that if the group is quasi-split, then every isogeny class contains the reduction of a CM point,
Pol van Hoften
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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
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Calabi–Yau attractor varieties and degeneration of Hodge structure

Open Physics
We present an application of asymptotic Hodge theory to the study of the attractor locus in flux compactifications. Our strategy is to investigate attractor points arising at the boundary of moduli spaces, where the limiting mixed Hodge structures encode
Rahmati Mohammad Reza
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F-zips with additional structure on splitting models of Shimura varieties

Forum of Mathematics, Sigma
We construct universal G-zips on good reductions of the Pappas-Rapoport splitting models for PEL-type Shimura varieties. We study the induced Ekedahl-Oort stratification, which sheds new light on the mod p geometry of splitting models.
Xu Shen, Yuqiang Zheng
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Integral models of Shimura varieties with parahoric level structure, II

Forum of Mathematics, Pi
We construct integral models of Shimura varieties of abelian type with parahoric level structure over odd primes. These models are étale locally isomorphic to corresponding local models.
Mark Kisin, Georgios Pappas, Rong Zhou
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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
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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
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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
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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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