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Fat chance : probability from 0 to 1 / Benedict Gross, Joe Harris, Emily Riehl. [elektronicky zdroj]
Autor:
Gross, Benedict H., 1950-, author
Externí odkaz:
Kolekce e-knih KNAV
Autor:
Gross, Benedict H., Dasgupta, Samit
In this note we describe our personal encounters with the $p$-adic Stark conjecture. Gross describes the period between $1977$ and $1986$ when he came to formulate these conjectures (\S 1-8), and Dasgupta describes the period between $1998$ and $2021
Externí odkaz:
http://arxiv.org/abs/2303.03299
In an earlier work, we considered a family of restriction problems for classical groups (over local and global fields) and proposed precise answers to these problems using the local and global Langlands correspondence. These restriction problems were
Externí odkaz:
http://arxiv.org/abs/2204.10108
Autor:
Gross, Benedict H
In this paper, we survey some mathematical developments that followed from the discovery of simple supercuspidal representations of p-adic groups.
Externí odkaz:
http://arxiv.org/abs/2005.09078
Autor:
Gross, Benedict H
In this paper, we introduce the notion of incoherent definite orthogonal and Hermitian spaces, and use their neighboring spaces as a tool for the local study of orthogonal and unitary Shimura varieties. This generalizes earlier work, using incoherent
Externí odkaz:
http://arxiv.org/abs/2005.05188
Autor:
Gross, Benedict H
In this expository paper, we review the formula of Chowla and Selberg for the periods of elliptic curves with complex multiplication, and discuss two methods of proof. One uses Kronecker's limit formula and the other uses the geometry of a family of
Externí odkaz:
http://arxiv.org/abs/2005.04194
Publikováno v:
Compositio Math. 156 (2020) 2298-2367
This paper generalizes the GGP conjectures which were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the nongeneric L-packets arising from Arthur parameters. The paper introduces the key notion o
Externí odkaz:
http://arxiv.org/abs/1911.02783
Autor:
Gross, Benedict H., Garibaldi, Skip
Publikováno v:
In Indagationes Mathematicae September 2021 32(5):987-1004
A hyperelliptic curve over $\mathbb Q$ is called "locally soluble" if it has a point over every completion of $\mathbb Q$. In this paper, we prove that a positive proportion of hyperelliptic curves over $\mathbb Q$ of genus $g\geq 1$ are locally solu
Externí odkaz:
http://arxiv.org/abs/1310.7692
Let $k$ be a field, let $G$ be a reductive group, and let $V$ be a linear representation of $G$. Let $V//G = Spec(Sym(V^*))^G$ denote the geometric quotient and let $\pi: V \to V//G$ denote the quotient map. Arithmetic invariant theory studies the ma
Externí odkaz:
http://arxiv.org/abs/1310.7689