Arithmetic, Geometry, Cryptography and Coding Theory.

Format:

Book

Author/Creator:

Ballet, Stéphane.

Contributor:

Bisson, Gaetan.

Bouw, Irene.

Series:

Contemporary Mathematics

Contemporary Mathematics ; v.770

Language:

English

Subjects (All):

Coding theory--Congresses.

Coding theory.

Geometry, Algebraic--Congresses.

Geometry, Algebraic.

Cryptography--Congresses.

Cryptography.

Number theory--Congresses.

Number theory.

Physical Description:

1 online resource (322 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2021.

Summary:

This volume contains the proceedings of the 17th International Conference on Arithmetic, Geometry, Cryptography and Coding Theory (AGC2T-17), held from June 10-14, 2019, at the Centre International de Rencontres Mathématiques in Marseille, France. The conference was dedicated to the memory of Gilles Lachaud, one of the founding fathers of the AGC2T series.Since the first meeting in 1987 the biennial AGC2T meetings have brought together the leading experts on arithmetic and algebraic geometry, and the connections to coding theory, cryptography, and algorithmic complexity. This volume highlights important new developments in the field.

Contents:

Cover

Title page

Contents

Preface

A new upper bound for the largest complete \boldmath( , )-arc in \boldmath\PG(2, )

1. Introduction

2. Some basic equations

3. Non-existence of some \boldmath( , )-arcs in \boldmath\PG(2, )

4. New largest bound

5. Application of Theorem 4.1

Acknowledgment

References

Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces

2. Background

3. The minimum distance of codes over some families of algebraic surfaces

4. Four improvements

5. An example: surfaces in \boldmathℙ³

Acknowledgments.

On the number of effective divisors in algebraic function fields defined over a finite field

2. Contents

3. Non-asymptotical case

4. Asymptotical case

Appendix A.

The absolute discriminant of the endomorphism ring of most reductions of a non-CM elliptic curve is close to maximal

2. Proof of the main theorem

Acknowledgments

Toward good families of codes from towers of surfaces

Introduction

1. Codes from surfaces

2. Infinite étale towers of surfaces

3. Open problems

Appendix A. On the étale site of marked schemes, \normalfont by Alexander Schmidt

Sato-Tate groups of abelian threefolds: a preview of the classification

2. Background on Sato-Tate groups

3. Classification: an overview

4. Realization

Arithmetic, Geometry, and Coding Theory: Homage to Gilles Lachaud

1. Gilles Lachaud's early works

2. Gilles Lachaud: friend and mathematician

3. A Tribute to Gilles Lachaud

4. Gilles Lachaud's work

References.

Elliptic curves with large Tate-Shafarevich groups over \boldmath _{ }( )

1. Invariants of elliptic curves over function fields

2. The elliptic curves \boldmath _{ , }

3. Preliminaries on character sums

4. The \boldmath -function of \boldmath _{ , }

5. Non-vanishing of \boldmath ( _{ , }, ) at the central point and consequences

6. Distribution of the Kloosterman sums \Kloosnᵧ( )

7. Estimates of the central value ( _{ , }, ⁻¹)

8. Proof of Theorem C

On Sato-Tate distributions, extremal traces, and real multiplication in genus 2

2. Background and notation

3. Weyl integration formula

4. Taylor expansions for the trace function

5. On results of Lachaud

6. Distribution of extremal traces in families

7. Conclusion

La trace et le deltoïde de \boldmath\SU(3)

2. Le groupe unitaire

3. Le deltoïde

4. Loi du caractère standard

5. Loi de la longueur de la trace

6. Loi de la norme de la trace

7. Loi du caractère de la représentation adjointe

8. Loi de la partie réelle du caractère standard

9. Loi de la partie imaginaire du caractère standard

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Stable models of plane quartics with hyperelliptic reduction

1. Introduction and main result

2. Link with theta constants

3. A Riemann model providing a good \PHM

4. Bitangents of a smooth plane quartic

5. The algorithm and an example

Courbes de genre \boldmath3 avec \boldmath ₃ comme groupe d'automorphismes

2. Caractéristique différente de 2 et 3

3. Le cas de caractéristique 3

Bornes sur le nombre de points rationnels des courbes : en quête d'uniformité

2. Comptage euclidien.

3. Variante de Lang-Silverman

Appendice A. Corrigendum à "Minorations des hauteurs normalisées des sous-variétés de variétés abéliennes II" par Sinnou David et Patrice Philippon

The quadratic hull of a code and the geometric view on multiplication algorithms

2. Multiplication reductions

3. An example in dimension 2

4. The canonical point

5. The quadratic hull

6. Application to geometric realizations

7. Experimental results

8. Further properties of the quadratic hull

Serre's genus fifty example

2. The elliptic curve

3. Constructing the curve via Artin-Schreier extensions

4. More equations and intermediate curves

Back Cover.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.

ISBN:

9781470464264

1470464268

OCLC:

1259589984