# Analogues of Brauer-Siegel theorem in arithmetic geometry

@article{Hindry2019AnaloguesOB, title={Analogues of Brauer-Siegel theorem in arithmetic geometry}, author={Marc Hindry}, journal={Arithmetic Geometry: Computation and Applications}, year={2019} }

We will explain analogies between the classical Brauer-Siegel theorem, a statement relating asymptotically the class number, regulator of units and discriminant of a number field, and similar statement involving arithmetic invariants of algebraic varieties over a finite or global field. We present precisely the analogy for surfaces over a finite field and for abelian varieties over a global field (i.e. a number field or the function field of a cuve over a finite field), surveying some recent…

## 4 Citations

Elliptic curves with large Tate–Shafarevich groups over Fq(t)

- Mathematics
- 2020

Let Fq be a finite field of odd characteristic p. We exhibit elliptic curves over the rational function field K = Fq(t) whose Tate-Shafarevich groups are large. Precisely, we consider certain…

N T ] 3 0 Ju l 2 01 9 Elliptic curves with large Tate – Shafarevich groups over F q ( t )

- Mathematics
- 2019

Let Fq be a finite field of odd characteristic p. We exhibit elliptic curves over the rational function field K = Fq(t) whose Tate-Shafarevich groups are large. More precisely, we consider certain…

Sur le th\'eor\`eme de Brauer--Siegel g\'en\'eralis\'e

- Mathematics
- 2021

We exhibit new sets of conditions which ensure that a family of number fields unconditionally satisfies the Brauer–Siegel theorem, as generalised by Tsfasman and Vladuts. We also give a few explicit…

Elliptic curves with large Tate-Shafarevich groups over $\mathbb{F}_q(t)$

- Mathematics
- 2019

Let $\mathbb{F}_q$ be a finite field of odd characteristic $p$. We exhibit elliptic curves over the rational function field $K = \mathbb{F}_q(t)$ whose Tate-Shafarevich groups are large. More…

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Hindry has proposed an analogue of the classical Brauer-Siegel theorem for abelian varieties over global fields. Roughly speaking, it says that the product of the regulator of the Mordell-Weil group…

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Consider a family of abelian varieties Ai of fixed dimension defined over the function field of a curve over a finite field. We assume finiteness of the Shafarevic-Tate group of Ai. We ask then when…

Analogues of Brauer-Siegel theorem in arithmetic geometry. Arithmetic geometry: computation and applications, Contemp

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