Arithmetic Moduli of Elliptic Curves. (AM-108), Volume 108Princeton University Press, 2 de mar. de 2016 - 528 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
| 3 | |
REVIEW OF ELLIPTIC CURVES | 63 |
THE FOUR BASIC MODULI PROBLEMS FOR ELLIPTIC CURVES SORITES | 98 |
THE FORMALISM OF MODULI PROBLEMS | 107 |
Regularity theorems | 129 |
CYCLICITY | 152 |
QUOTIENTS BY FINITE GROUPS | 186 |
COARSE MODULI SCHEMES CUSPS AND COMPACTIFICATIONS | 224 |
THE CALCULUS OF CUSPS AND COMPONENTS VIA THE GROUPS TN AND THE GLOBAL STRUCTURE OF THE BASIC MODULI PROBLE... | 286 |
INTERLUDE EXOTIC MODULAR MORPHISMS AND ISOMORPHISMS | 339 |
NEW MODULI PROBLEMS IN CHARACTERISTIC p IGUSA CURVES | 344 |
REDUCTIONS mod p OF THE BASIC MODULI PROBLEMS | 389 |
APPLICATION TO THEOREMS OF GOOD REDUCTION | 457 |
NOTES ADDED IN PROOF | 505 |
REFERENCES | 511 |
MODULI PROBLEMS VIEWED OVER CYCLOTOMIC INTEGER RINGS | 271 |
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Termos e frases comuns
action acts affine apply arbitrary assertion base canonical characteristic closed subscheme commutative complete condition connected Consider corresponding cusps cyclic defined denote diagram Drinfeld effective Cartier divisor element Ell/R elliptic curve equality equation equivalent exact order exact sequence exists extension fact factorization fiber field finite and flat finite etale finite flat finite locally free flat functor geometric given group-scheme holds homomorphism hypothesis induced integer invertible isogeny isomorphism LEMMA moduli problem morphism natural noetherian normal operates ordinary pair parameter prime Proof proper PROPOSITION prove quotient rank reduced regular relatively representable representable moduli problem represented result ring root S-scheme satisfies scheme smooth curve Spec standard structure subgroup suffices supersingular points Suppose surjective THEOREM trivial unique universal Z/NZ zero