Documents  11G20 | enregistrements trouvés : 43

- 226 p.
ISBN 978-0-8218-0925-9

Contemporary mathematics , 0245

Localisation : Collection 1er étage

borne de Weil # corps arithmétique # courbe algébrique # couverture p # fontion zeta # formule de trace # groupe monodromique # géométrie algébrique # théorie des nombres

11G09 ; 11G18 ; 11G20 ; 11R58

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- 215 p.
ISBN 978-2-85629-175-7

Séminaires et congrès , 0011

Localisation : Collection 1er étage

fonction zêta # variété abélienne # corps de fonction # courbe sur les corps fini # tour de corps de fonction # corps fini # graphe # semi-groupe numérique # polynôme sur les corps finis # cryptographie # courbe hyperelliptique # représentation p-adique # tour de corps de classe # groupe de Galois # point rationel # fraction continue # régulateur # nombre de classe d'idéaux # complexité bilinéaire # jacobienne hyperelliptique

14H05 ; 14G05 ; 11G20 ; 20M99 ; 94B27 ; 11T06 ; 11T71 ; 11R37 ; 14G10 ; 14G15 ; 11R58 ; 11A55 ; 11R42 ; 11Yxx ; 12E20 ; 14H40 ; 14K05

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- 183 p.
ISBN 978-0-8218-3365-0

Proceedings of symposia in applied mathematics , 0062

Localisation : Collection 1er étage

cryptographie # clé publique # preuve de sécurité # courbe elliptique # algorithme LLL # NTRU

54C40 ; 14E20 ; 14G50 ; 11G20 ; 11T71 ; 11Yxx ; 94Axx ; 46E25 ; 20C20

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- vii; 206 p.
ISBN 978-0-8218-4716-9

Contemporary mathematics , 0487

Localisation : Collection 1er étage

théorie des nombres # géométrie algébrique # cryptographie # théorie des codes correcteurs d'erreurs

11G10 ; 11G20 ; 14G10 ; 14G15 ; 14G50 ; 14Q05 ; 11M38 ; 11R42 ; 11-06 ; 14-06 ; 94-06 ; 94A60 ; 94Bxx ; 11Txx ; 00B25

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- vii; 166 p.
ISBN 978-0-8218-4955-2

Contemporary mathematics , 0521

Localisation : Collection 1er étage

théorie des nombres # géométrie algébrique # géométrie algébrique arithmétique # géométrie diophantienne # courbe algébrique # cryptographie

11G10 ; 11G15 ; 11G20 ; 14G10 ; 14G15 ; 14G50 ; 14H05 ; 14H10 ; 14H45 ; 14Q05 ; 11-06 ; 14-06 ; 94-06 ; 00B25 ; 11Gxx ; 14Gxx ; 14Hxx ; 94A60

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- xii; 129 p.
ISBN 978-0-8218-4320-8

Contemporary mathematics , 0463

Localisation : Collection 1er étage

géométrie algébrique arithmétique # théorie des nombes algébriques

14G05 ; 14G10 ; 14G15 ; 14G50 ; 14H45 ; 11G50 ; 11G15 ; 11G20 ; 11Y16 ; 11F11 ; 11-02 ; 14-06 ; 14Qxx ; 11Gxx ; 00B25

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- vii-183 p.
ISBN 978-0-8218-7572-8

Contemporary mathematics , 0574

Localisation : Collection 1er étage

arithmétique # géométrie # cryptographie # codage # variétés abéliennes # théorie de la dimension

11-06 ; 14-06 ; 11G10 ; 11G20 ; 11M38 ; 11R42 ; 11T71 ; 14G10 ; 14G15 ; 14G50 ; 14Q05 ; 00B25

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- pag. mult.

Séminaire Bourbaki mars 2014

Localisation : Séminaire 1er étage

conjecture de Tate # surfaces K3 # ultramétricité # théorie des verres de spin # théorie cinétique des gaz # équation de Boltzmann # nombres premiers dans les progressions arithmétiques

11G20 ; 82D30 ; 82B40 ; 82C40 ; 76P05 ; 11N13

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- v; 306 p.
ISBN 978-1-4704-1461-0

Contemporary mathematics , 0637

Localisation : Collection 1er étage

théorie des codes # géométrie algébrique # cryptographie # théorie des nombres

11G10 ; 11G20 ; 11G25 ; 11Y16 ; 14G05 ; 14G15 ; 14Q05 ; 14Q15 ; 94B27

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- viii; 238 p.
ISBN 978-1-4704-1947-9

Contemporary mathematics , 0663

Localisation : Collection 1er étage

distribution de Frobenius # conjecture de Sato-Tate # conjecture de Lang-Trotter

11G05 ; 11G10 ; 11G20 ; 11G25 ; 11M50 ; 11N05 ; 11R44 ; 14G10 ; 14G25

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- v; 199 p.
ISBN 978-1-4704-2810-5

Contemporary mathematics , 0686

Localisation : Collection 1er étage

arithmétique # géométrie # cryptographie # codage # variété abélienne

11-06 ; 11G20 ; 11G25 ; 11T71 ; 14G15 ; 14H40 ; 94A60 ; 94B27 ; 00B25

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- vi; 175 p.
ISBN 978-1-4704-4212-5

Contemporary mathematics , 0722

Localisation : Collection 1er étage

théorie des nombres # théorie des codes # cryptographie # géométrie arithmétique # cohomologie de De Rham # fonction zeta

11G20 ; 11G30 ; 11G32 ; 11G40 ; 11T71 ; 14G10 ; 14H40 ; 14Q05 ; 20C20 ; 20G41

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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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Research talks;Algebraic and Complex Geometry;Number Theory

We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin’s conjecture for primitive roots.

11G20 ; 14H52 ; 11Y16 ; 11T23

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Research talks;Algebraic and Complex Geometry;Number Theory

Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise. Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to ...

11G20 ; 11G35 ; 14G05

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Research talks;Algebraic and Complex Geometry;Number Theory

Consider an ordinary isogeny class of elliptic curves over a finite, prime field. Inspired by a random matrix heuristic (which is so strong it's false), Gekeler defines a local factor for each rational prime. Using the analytic class number formula, he shows that the associated infinite product computes the size of the isogeny class.
I'll explain a transparent proof of this formula; it turns out that this product actually computes an adelic orbital integral which visibly counts the desired cardinality. Moreover, the new perspective allows a natural generalization to higher-dimensional abelian varieties. This is joint work with Julia Gordon and S. Ali Altug. Consider an ordinary isogeny class of elliptic curves over a finite, prime field. Inspired by a random matrix heuristic (which is so strong it's false), Gekeler defines a local factor for each rational prime. Using the analytic class number formula, he shows that the associated infinite product computes the size of the isogeny class.
I'll explain a transparent proof of this formula; it turns out that this product actually computes an adelic ...

11G20 ; 22E35 ; 14G15

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Research talks;Algebraic and Complex Geometry;Number Theory

Curves over finite fields of large genus with many rational points have been of interest for both theoretical reasons and for applications. In the past, various methods have been employed for the construction of such curves. One such method is by means of explicit recursive equations and will be the emphasis of this talk.The first explicit examples were found by Garcia-Stichtenoth over quadratic finite fields in 1995. Afterwards followed the discovery of good towers over cubic finite fields and finally all nonprime finite fields in 2013 (B.-Beelen-Garcia-Stichtenoth). The recursive nature of these towers makes them very special and in fact all good examples have been shown to have a modular interpretation of some sort. The questions of finding good recursive towers over prime fields resisted all attempts for several decades and lead to the common belief that such towers might not exist. In this talk I will try to give an overview of the landscape of explicit recursive towers and present a recently discovered tower over all finite fields including prime fields, except $F_{2}$ and $F_{3}$.
This is joint work with Christophe Ritzenthaler. Curves over finite fields of large genus with many rational points have been of interest for both theoretical reasons and for applications. In the past, various methods have been employed for the construction of such curves. One such method is by means of explicit recursive equations and will be the emphasis of this talk.The first explicit examples were found by Garcia-Stichtenoth over quadratic finite fields in 1995. Afterwards followed the ...

11G20 ; 11T71 ; 14H25 ; 14G05 ; 14G15

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Research talks;Algebraic and Complex Geometry;Number Theory

I will give an account of some aspects of the mathematical work of Gilles Lachaud, especially the work in which I was associated with him. This will be mixed with some personal reminiscences.

11G25 ; 11T71 ; 11G20

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- 204 p.
ISBN 978-0-521-65374-9

London mathematical society lecture note series , 0265

Localisation : Collection 1er étage

algorithme # application des courbes elliptiques # arithmétique # courbe elliptique # mathématique discrète # problème logarithmique

11G20 ; 11Gxx ; 11T71 ; 68P25 ; 94A60

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