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What is Arithmetic Geometry: Computation and Applications about?

Cover 1 Title page 2 Contents 4 Preface 6 Hasse–Witt and Cartier–Manin matrices: A warning and a request 8 Prologue 8 1. Matrices and semilinear algebra 10 2. Hasse–Witt and Cartier–Manin matrices 12 3. Cartier–Manin matrices for hyperelliptic curves 14 4. Hasse–Witt matrices through the ages 16 5. Subsequent developments 18 6. Conclusion 20 References 20 Works that cite Manin (1961) or Yui (1978) 21 Analogues of Brauer-Siegel theorem in arithmetic geometry 26 Introduction 26 1. Classical Brauer-Siegel theorems 27 2. Zeta and L-functions 31 3. Abelian varieties and surfaces 34 4. Generalisations 38 5. Theorems and conjectures of Brauer-Siegel type 42 References 46 The Belyi degree of a curve is computable 50 1. Introduction 50 Acknowledgements 51 2. The Belyi degree 51 3. First proof of Theorem 1.2 54 4. Second proof of Theorem 1.2 59 5. The Fermat curve of degree four 60 References 63 Weight enumerators of Reed-Muller codes from cubic curves and their duals 66 1. Introduction 66 2. Singular projective plane cubic curves 70 3. Smooth projective plane cubic curves 71 4. Low-weight coefficients of W_{C_{2,3}^{\perp}}(X,Y) 74 5. Singular affine plane cubic curves 76 6. Smooth affine p

Author

Yves Aubry, Everett W. Howe and Christophe Ritzenthaler, editors

Language

EN