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Modular curves and the eisenstein ideal
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Arithmetic moduli of elliptic curves
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"
Rational isogenies of prime degree
In this table, g is the genus of Xo(N), and v the number of noncuspidal rational points of Xo(N) (which is, in effect, the number of rational N-isogenies classified up to "twist"). For an excellent
Deforming Galois Representations
Given a continuous homomorphism $${G_{Q,S}}G{L_2}\left( {{Z_p}} \right)$$ where Gℚ,S is the Galois group of the maximal algebraic extension of ℚ unramified outside the finite set S of primes of
Class fields of abelian extensions of Q
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 0. Notation and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Canonical Height Pairings via Biextensions
The object of this paper is to present the foundations of a theory of p-adic-valued height pairings $$A\left( K \right) \times A'\left( K \right) \to {Q_p}$$ (*) , where Λ is a abelian
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