Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields
Forum of Mathematics, Pi, 2022 Given a K3 surface X over a number field K with potentially good reduction everywhere, we prove that the set of primes of K where the geometric Picard rank jumps is infinite.
Ananth N. Shankar +3 more
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Chow groups and L-derivatives of automorphic motives for unitary groups, II.
Forum of Mathematics, Pi, 2022 In this article, we improve our main results from [LL21] in two directions: First, we allow ramified places in the CM extension $E/F$ at which we consider representations that are spherical with respect to a certain special maximal compact subgroup, by ...
Chao Li, Yifeng Liu
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CM liftings of $K3$ surfaces over finite fields and their applications to the Tate conjecture
Forum of Mathematics, Sigma, 2021 We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of $K3$ surfaces over finite fields.
Kazuhiro Ito +2 more
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Grassmanniennes affines tordues sur les entiers
Forum of Mathematics, Sigma, 2023 We generalize the works of Pappas–Rapoport–Zhu on twisted affine Grassmannians to the wildly ramified case under mild assumptions. This rests on a construction of certain smooth affine $\mathbb {Z}[t]$ -groups with connected fibers of parahoric ...
João Lourenço
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Normalizers of intermediate congruence subgroups of the Hecke subgroups
Open Mathematics, 2017 For a square-free positive integer N, we study the normalizer of ΓΔ(N) in PSL2(ℝ) and investigate the group structure of its quotient by ΓΔ(N) under certain conditions.
Im Bo-Hae, Jeon Daeyeol, Kim Chang Heon
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ANDRÉ–OORT CONJECTURE AND NONVANISHING OF CENTRAL $L$ -VALUES OVER HILBERT CLASS FIELDS
Forum of Mathematics, Sigma, 2016 Let $F/\mathbf{Q}$ be a totally real field and $K/F$ a ...
ASHAY A. BURUNGALE, HARUZO HIDA
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ENLARGED MIXED SHIMURA VARIETIES, BI-ALGEBRAIC SYSTEM AND SOME AX TYPE TRANSCENDENTAL RESULTS
Forum of Mathematics, Sigma, 2019 We develop a theory of enlarged mixed Shimura varieties, putting the universal vectorial bi-extension defined by Coleman into this framework to study some functional transcendental results of Ax type. We study their bi-algebraic systems, formulate the Ax-
ZIYANG GAO
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Vanishing theorems for the mod p cohomology of some simple Shimura varieties
Forum of Mathematics, Sigma, 2020 We show that the mod p cohomology of a simple Shimura variety treated in Harris-Taylor’s book vanishes outside a certain nontrivial range after localizing at any non-Eisenstein ideal of the Hecke algebra. In cases of low dimensions, we show the vanishing
Teruhisa Koshikawa
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Semi-stable and splitting models for unitary Shimura varieties over ramified places. I.
Forum of Mathematics, SigmaWe consider Shimura varieties associated to a unitary group of signature $(n-s,s)$ where n is even. For these varieties, we construct smooth p-adic integral models for $s=1$ and regular p-adic integral models for $s=2$ and $s=3$
Ioannis Zachos, Zhihao Zhao
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Mod p points on shimura varieties of parahoric level
Forum of Mathematics, PiWe 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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