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Documents  Gekeler, Ernst-Ulrich | enregistrements trouvés : 3

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Research talks;Algebraic and Complex Geometry;Number Theory

We construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type $\mathbf{GL}(r)$ over finite rings $(r\ge 3)$ instead of $\mathbf{GL}(2)$. In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational points/genus". The construction relies on higher-rank Drinfeld modular varieties and the supersingular trick and uses mainly rigid- analytic techniques. We construct curves over finite fields with properties similar to those of classical elliptic or Drinfeld modular curves (as far as elliptic points, cusps, ramification, ... are concerned), but whose coverings have Galois groups of type $\mathbf{GL}(r)$ over finite rings $(r\ge 3)$ instead of $\mathbf{GL}(2)$. In the case where the finite field is non-prime, there results an abundance of series or towers with a large ratio "number of rational ...

11G09 ; 11G20 ; 14G15

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- 431 p.
ISBN 978-3-540-17201-7

Lecture notes in mathematics , 1231

Localisation : Collection 1er étage

corps de fonctions algébriques # courbe # groupe arithmétique # groupe modulaire

10D12 ; 10DO7 ; 12A90 ; 14H25

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- 142 p.

Bonner mathematische schriften , 0119

Localisation : Publication 1er étage

10D12

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