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Twisted L-functions and monodromy [[electronic resource] /] / by Nicholas M. Katz



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Autore: Katz Nicholas M. <1943-> Visualizza persona
Titolo: Twisted L-functions and monodromy [[electronic resource] /] / by Nicholas M. Katz Visualizza cluster
Pubblicazione: Princeton, : Princeton University Press, 2002
Edizione: Core Textbook
Descrizione fisica: 1 online resource (258 p.)
Disciplina: 512/.74
Soggetto topico: L-functions
Monodromy groups
Soggetto non controllato: Abelian variety
Absolute continuity
Addition
Affine space
Algebraically closed field
Ambient space
Average
Betti number
Birch and Swinnerton-Dyer conjecture
Blowing up
Codimension
Coefficient
Computation
Conjecture
Conjugacy class
Convolution
Critical value
Differential geometry of surfaces
Dimension (vector space)
Dimension
Direct sum
Divisor (algebraic geometry)
Divisor
Eigenvalues and eigenvectors
Elliptic curve
Equation
Equidistribution theorem
Existential quantification
Factorization
Finite field
Finite group
Finite set
Flat map
Fourier transform
Function field
Functional equation
Goursat's lemma
Ground field
Group representation
Hyperplane
Hypersurface
Integer matrix
Integer
Irreducible component
Irreducible polynomial
Irreducible representation
J-invariant
K3 surface
L-function
Lebesgue measure
Lefschetz pencil
Level of measurement
Lie algebra
Limit superior and limit inferior
Minimal polynomial (field theory)
Modular form
Monodromy
Morphism
Numerical analysis
Orthogonal group
Percentage
Polynomial
Prime number
Probability measure
Quadratic function
Quantity
Quotient space (topology)
Representation theory
Residue field
Riemann hypothesis
Root of unity
Scalar (physics)
Set (mathematics)
Sheaf (mathematics)
Subgroup
Summation
Symmetric group
System of imprimitivity
Theorem
Trivial representation
Zariski topology
Classificazione: SI 830
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references (p. [235]-239) and index.
Nota di contenuto: pt. 1. Background material -- pt. 2. Twist sheaves, over an algebraically closed field -- pt. 3. Twist sheaves, over a finite field -- pt. 4. Twist sheaves over schemes of finite type over Z.
Sommario/riassunto: For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
Titolo autorizzato: Twisted L-Functions and Monodromy  Visualizza cluster
ISBN: 1-282-82089-3
9786612820892
1-4008-2488-5
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910785573203321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; no. 150.