Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 /

The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry,...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Katz, Nicholas M. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton, NJ : Princeton University Press, [2016]
Colección:Annals of Mathematics Studies ; 116
Temas:
Gaussian sums.
Homology theory.
Kloosterman sums.
Monodromy groups.
MATHEMATICS / Number Theory.
Abelian category.
Absolute Galois group.
Absolute value.
Additive group.
Adjoint representation.
Affine variety.
Algebraic group.
Automorphic form.
Automorphism.
Big O notation.
Cartan subalgebra.
Characteristic polynomial.
Classification theorem.
Coefficient.
Cohomology.
Cokernel.
Combination.
Commutator.
Compactification (mathematics).
Complex Lie group.
Complex number.
Conjugacy class.
Continuous function.
Convolution theorem.
Convolution.
Determinant.
Diagonal matrix.
Dimension (vector space).
Direct sum.
Dual basis.
Eigenvalues and eigenvectors.
Empty set.
Endomorphism.
Equidistribution theorem.
Estimation.
Exactness.
Existential quantification.
Exponential sum.
Exterior algebra.
Faithful representation.
Finite field.
Finite group.
Four-dimensional space.
Frobenius endomorphism.
Fundamental group.
Fundamental representation.
Galois group.
Gauss sum.
Homomorphism.
Integer.
Irreducibility (mathematics).
Isomorphism class.
Kloosterman sum.
L-function.
Leray spectral sequence.
Lie algebra.
Lie theory.
Maximal compact subgroup.
Method of moments (statistics).
Monodromy theorem.
Monodromy.
Morphism.
Multiplicative group.
Natural number.
Nilpotent.
Open problem.
P-group.
Pairing.
Parameter space.
Parameter.
Partially ordered set.
Perfect field.
Point at infinity.
Polynomial ring.
Prime number.
Quotient group.
Representation ring.
Representation theory.
Residue field.
Riemann hypothesis.
Root of unity.
Sheaf (mathematics).
Simple Lie group.
Skew-symmetric matrix.
Smooth morphism.
Special case.
Spin representation.
Subgroup.
Support (mathematics).
Symmetric matrix.
Symplectic group.
Symplectic vector space.
Tensor product.
Theorem.
Trace (linear algebra).
Trivial representation.
Variable (mathematics).
Weil conjectures.
Weyl character formula.
Zariski topology.
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Tabla de Contenidos:
  • Frontmatter
  • Contents
  • Introduction
  • CHAPTER 1. Breaks and Swan Conductors
  • CHAPTER 2. Curves and Their Cohomology
  • CHAPTER 3. Equidistribution in Equal Characteristic
  • CHAPTER 4. Gauss Sums and Kloosterman Sums: Kloosterman Sheaves
  • CHAPTER 5. Convolution of Sheaves on Gm
  • CHAPTER 6. Local Convolution
  • CHAPTER 7. Local Monodromy at Zero of a Convolution: Detailed Study
  • CHAPTER 8. Complements on Convolution
  • CHAPTER 9. Equidistribution in (S1)r of r-tuples of Angles of Gauss Sums
  • CHAPTER 10. Local Monodromy at ∞ of Kloosterman Sheaves
  • CHAPTER 11. Global Monodromy of Kloosterman Sheaves
  • CHAPTER 12. Integral Monodromy of Kloosterman Sheaves (d'après O. Gabber)
  • CHAPTER 13. Equidistribution of "Angles" of Kloosterman Sums
  • References

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