منابع مشابه
Euler characteristics and elliptic curves.
Let E be a modular elliptic curve over [symbol, see text], without complex multiplication; let p be a prime number where E has good ordinary reduction; and let Finfinity be the field obtained by adjoining [symbol, see text] to all p-power division points on E. Write Ginfinity for the Galois group of Finfinity over [symbol, see text]. Assume that the complex L-series of E over [symbol, see text]...
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Let E/Q be a modular elliptic curve, and p > 3 a good ordinary or semistable prime. Under mild hypotheses, we prove an exact formula for the μ-invariant associated to the weight-deformation of the Tate module of E. For example, at ordinary primes in the range 3 < p < 100, the result implies the triviality of the μ-invariant of X0(11). 2000 Mathematics Subject Classification: 11G40; also 11F33, ...
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This paper consists of two parts. In the first we present a general theory of Euler systems. The main results (see §§3 and 4) show that an Euler system for a p-adic representation T gives a bound on the Selmer group associated to the dual module Hom(T, μp∞). These theorems, which generalize work of Kolyvagin [Ko], have been obtained independently by Kato [Ka1], Perrin-Riou [PR2], and the author...
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Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1, . . . , Pn are points on E defined over K. To this information we associate an ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1997
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.94.21.11115