Arithmetic Moduli of Elliptic Curves

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Princeton University Press, 21 de fev. de 1985 - 514 páginas

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.

 

Conteúdo

GENERALITIES ON ASTRUCTURES
3
REVIEW OF ELLIPTIC CURVES
63
THE FOUR BASIC MODULI PROBLEMS
98
THE FORMALISM OF MODULI PROBLEMS
107
MORE ON RIGIDITY AND REPRESENTABILITY
125
CYCLICITY
152
QUOTIENTS BY FINITE GROUPS
186
BASE CHANGE FOR RINGS OF INVARIANTS
215
MODULI PROBLEMS VIEWED OVER CYCLOTOMIC
271
THE CALCULUS OF CUSPS AND COMPONENTS
286
INTERLUDE EXOTIC MODULAR MORPHISMS
339
REDUCTIONS mod p OF THE BASIC MODULI
389
APPLICATION TO THEOREMS OF GOOD REDUCTION
457
NOTES ADDED IN PROOF
505
REFERENCES
511
Direitos autorais

COARSE MODULI SCHEMES CUSPS
224

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