Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Shankar, Ananth N."'
We prove that Shimura varieties admit integral canonical models for sufficiently large primes. In the case of abelian-type Shimura varieties, this recovers work of Kisin-Kottwitz for sufficiently large primes. We also prove the existence of integral
Externí odkaz:
http://arxiv.org/abs/2405.12392
We prove that Shimura varieties of abelian type satisfy a $p$-adic Borel-extension property over discretely valued fields. More precisely, let $\mathsf{D}$ denote the rigid-analytic closed unit disc and $\mathsf{D}^{\times} = \mathsf{D} \setminus \{0
Externí odkaz:
http://arxiv.org/abs/2310.06104
In this paper, we prove an intersection-theoretic result pertaining to curves in certain Hilbert modular surfaces in positive characteristic. Specifically, we show that given two appropriate curves C,D parameterizing abelian surfaces with real multip
Externí odkaz:
http://arxiv.org/abs/2209.02806
The main purpose of this work is to prove the Andr\'e-Oort conjecture in full generality.
Comment: Many details have been clarified and elaborated on, as well as minor errors corrected
Comment: Many details have been clarified and elaborated on, as well as minor errors corrected
Externí odkaz:
http://arxiv.org/abs/2109.08788
We prove two finiteness results for reductions of Hecke orbits of abelian varieties over local fields: one in the case of supersingular reduction and one in the case of reductive monodromy. As an application, we show that only finitely many abelian v
Externí odkaz:
http://arxiv.org/abs/2109.05147
Autor:
Shankar, Ananth N., Tsimerman, Jacob
We prove the existence of abelian varieties not isogenous to Jacobians over characterstic $p$ function fields. Our methods involve studying the action of degree $p$ Hecke operators on hypersymmetric points, as well as their effect on the formal neigh
Externí odkaz:
http://arxiv.org/abs/2105.02998
Let $\mathscr{X} \rightarrow C$ be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve $C$ in characteristic $p \geq 5$. We prove that the geometric Picard rank jumps at infinitely many closed points of $C$. More gener
Externí odkaz:
http://arxiv.org/abs/2011.08887
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. As a corollary, we prove that either $X_{\overline{K}}$ has infinitel
Externí odkaz:
http://arxiv.org/abs/1909.07473
In this article, we study the family of elliptic curves $E/\mathbb{Q}$, having good reduction at $2$ and $3$, and whose $j$-invariants are small. Within this set of elliptic curves, we consider the following two subfamilies: first, the set of ellipti
Externí odkaz:
http://arxiv.org/abs/1904.13063