Arithmetic Geometry: Computation and Applications: 16th International Conference on Arithmetic, Geometry, Cryptography, and Coding Theory, June 19-23, 2017, Centre International de Rencontres Mathematiques, Marseille, France

✍ Scribed by Yves Aubry; Everett W. Howe; Christophe Ritzenthaler

• Publisher: American Mathematical Society
• Year: 2019
• Tongue: English
• Leaves: 186
• Series: Contemporary Mathematics 722
• Category: Library

✦ Table of Contents

Cover
Title page
Contents
Preface
Hasse–Witt and Cartier–Manin matrices: A warning and a request
Prologue
1. Matrices and semilinear algebra
2. Hasse–Witt and Cartier–Manin matrices
3. Cartier–Manin matrices for hyperelliptic curves
4. Hasse–Witt matrices through the ages
5. Subsequent developments
6. Conclusion
References
Works that cite Manin (1961) or Yui (1978)
Analogues of Brauer-Siegel theorem in arithmetic geometry
Introduction
1. Classical Brauer-Siegel theorems
2. Zeta and 𝐿-functions
3. Abelian varieties and surfaces
4. Generalisations
5. Theorems and conjectures of Brauer-Siegel type
References
The Belyi degree of a curve is computable
1. Introduction
Acknowledgements
2. The Belyi degree
3. First proof of Theorem 1.2
4. Second proof of Theorem 1.2
5. The Fermat curve of degree four
References
Weight enumerators of Reed-Muller codes from cubic curves and their duals
1. Introduction
2. Singular projective plane cubic curves
3. Smooth projective plane cubic curves
4. Low-weight coefficients of 𝑊_{𝐶_{2,3}^{\perp}}(𝑋,𝑌)
5. Singular affine plane cubic curves
6. Smooth affine plane cubic curves
7. Low-weight coefficients of 𝑊_{(𝐶^{𝐴}_{2,3})^{\perp}}(𝑋,𝑌)
8. Acknowledgments
References
The distribution of the trace in the compact group of type 𝐆₂
1. Introduction
2. Exponential sums
3. The group \Gtwo and its Lie algebra
4. Real forms
5. The Steinberg map of \Gtwo
6. Maximal torus and alcove of \UGtwo
7. The Steinberg map on \UGtwo
8. The Weyl integration formula revisited
9. Image of the alcove
10. Distribution of the trace
11. Moments
References
The de Rham cohomology of the Suzuki curves
1. Introduction
2. The de Rham cohomology as a representation for the Suzuki group
3. The Dieudonné module and de Rham cohomology
4. An explicit basis for the de Rham cohomology
References
Décompositions en hauteurs locales
1. Introduction
2. Présentation des décompositions
3. Hauteurs globales, hauteurs locales
4. Modèles de Moret-Bailly des variétés abéliennes
5. Hauteur d’un point par la formule clef
6. Décomposition de la hauteur de Faltings d’une jacobienne hyperelliptique
7. Calculs explicites en dimension 1
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Using zeta functions to factor polynomials over finite fields
1. Introduction
2. Schoof’s algorithm
3. Kayal’s factoring idea
4. Pila’s algorithm
5. Generalization of Kayal’s factoring idea
6. A heuristic for Hypothesis Z
7. Weakening Hypothesis Z
8. Using varieties other than abelian varieties
Acknowledgements
References
Canonical models of arithmetic (1;∞)-curves
1. Uniformizations and orders
2. \Belyi maps
3. Canonical models
4. Modular interpretations
References
Maps between curves and arithmetic obstructions
1. Introduction
2. The fundamental group
3. Certifying non-isomorphism
4. Examples
5. Factoring polynomials over finite fields
References
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