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Computing the Brauer group of the product of two elliptic curves over a finite field
We discuss how to compute the Brauer group of the product of two elliptic curves over a finite field. Specifically, we apply the Artin–Tate formula...
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A twisted class number formula and Gross’s special units over an imaginary quadratic field
Let F / k be a finite abelian extension of number fields with k imaginary quadratic. Let O F be the ring of integers of F and n ⩾ 2 a rational integer....
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The Gross–Zagier–Zhang formula over function fields
We prove the Gross–Zagier–Zhang formula over global function fields of arbitrary characteristics. It is an explicit formula which relates the...
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Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case
We construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the middle cohomology of their reductions...
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The Tate conjecture, abelian varieties and K3 surfaces
M. Artin and J. Tate conjectured that the Brauer group of a smooth and projective variety over a finite field is a finite group. In his 1966 Bourbaki...
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Hazewinkel Functional Lemma and Classification of Formal Groups
AbstractThe main fields of application of formal groups are algebraic geometry and class field theory. The later uses both the classical Hilbert...
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Root Numbers of 5-adic Curves of Genus Two Having Maximal Ramification
The formulas for local root numbers of abelian varieties of dimension one are known. In this paper we treat the simplest unknown case in dimension...
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The work of Robert Langlands
A more accurate title might have been On the Work of Robert Langlands in Representation Theory, Automorphic Forms, Number Theory and Arithmetic...
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Chebotarev–Sato–Tate distribution for abelian surfaces potentially of \(\textrm{GL}_2\)-type
We state a hybrid Chebotarev–Sato–Tate conjecture for abelian varieties and we prove it in several particular cases using current potential...
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Introduction
In his youth, C.F. Gauss proved the law of quadratic reciprocity and further created the theory of genera for binary quadratic forms.
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On equivariant class formulas for Anderson modules
We obtain an equivariant class formula for z -deformation of Anderson modules. Under mild conditions, it allows us to get an equivariant class formula...
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Soergel Calculus with Patches
We adapt the diagrammatic presentation of the Hecke category to the dg category formed by the standard representatives for the Rouquier complexes. We...
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Class Field Theory
The letters of Emmy Noether show that she was strongly involved in the evolution of modern class field theory, obviously inspired by Hasse. When we...
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Elementary module associated to Selmer group of Artin representation
The functional equation for the Selmer group for an Artin representation was studied by Greenberg [
3 ,5 ], Greenberg and Vatsal [6 ] and Majumdar and...