Arithmetic Moduli of Elliptic CurvesPrinceton 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 |
COARSE MODULI SCHEMES CUSPS | 224 |
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Termos e frases comuns
abelian affine algebraically closed field assertion automorphism canonical isomorphism closed subscheme coarse moduli schemes commutative diagram complete local ring cusps cyclic subgroup defined degree denote disjoint union Drinfeld effective Cartier divisor element Ell/k Ell/R equation exact order fiber field of characteristic finite and flat finite etale finite flat finite group finite locally free finite presentation functor G-torsor G₁ galois geometric point given group-scheme Hom Surj homomorphism integer invertible invertible sheaf isogeny isomorphism Ker F kernel LEMMA modular morphism N)-structure N₁ noetherian open set pair parameter polynomial prime problem on E11/R Proof PROPOSITION Q.E.D. COROLLARY quotient R-algebra reduced regular relatively representable moduli representable moduli problem residue field root of unity S-group S-scheme set of sections sheaf short exact sequence smooth curve supersingular points Suppose surjective Tate THEOREM trivial unique Z/NZ Z/p¹Z