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Arithmetic Moduli of Elliptic Curves

Barry Mazur, Nicholas M. Katz

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ca. 149,99

Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "Fundamenta Nova" in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.

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Schlagwörter

Residue field, Theorem, Algebraically closed field, Morphism, Regularity theorem, Zariski topology, Prime factor, Axiom, Divisor, Cyclic group, Eigenfunction, Finite group, Coprime integers, Discrete valuation ring, Calculation, Subring, Algebraic variety, Integer, Disjoint union, Finite morphism, Canonical map, Congruence relation, Coefficient, Prime power, Cokernel, Elliptic curve, Neighbourhood (mathematics), Base change, Subgroup, Abelian variety, Factorization, Finite field, Level structure, Free module, Moduli space, Two-dimensional space, Change of base, Barry Mazur, Field of fractions, Commutative property, Representation theory, Diagram (category theory), One-parameter group, Ambient space, Open problem, Empty set, Irreducible component, Modular equation, Topology, Local ring, Group (mathematics), Noetherian, Arithmetic, Cusp form, Subset, Closed immersion, Dense set, Modular curve, Prime number, Riemann hypothesis, Coherent sheaf, Maximal ideal, Functor, Addition, Dimension, Q.E.D., Modular form, Special case, Corollary, Morphism of schemes