منابع مشابه
The main conjecture for CM elliptic curves at supersingular primes
At a prime of ordinary reduction, the Iwasawa “main conjecture” for elliptic curves relates a Selmer group to a p-adic L-function. In the supersingular case, the statement of the main conjecture is more complicated as neither the Selmer group nor the p-adic L-function is well-behaved. Recently Kobayashi discovered an equivalent formulation of the main conjecture at supersingular primes that is ...
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The Main Conjecture of Iwasawa theory for an elliptic curve E over Q and the anticyclotomic Zp-extension of an imaginary quadratic field K was studied in [BD2], in the case where p is a prime of ordinary reduction for E. Analogous results are formulated, and proved, in the case where p is a prime of supersingular reduction. The foundational study of supersingular main conjectures carried out by...
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Given a Galois extension L/K of number fields with Galois group G, a fundamental problem is to describe the (unramified) primes p of K whose Frobenius automorphisms lie in a given conjugacy class C of G. In particular, all such primes have the same splitting type in a sub-extension of L/K. In general, all that is known is that the primes have density |C|/|G| in the set of all primes, this being...
متن کاملPrimes, Elliptic Curves and Cyclic Groups: a Synopsis
The main question addressed in this paper focuses on the frequency with which the reductions modulo primes of a rational elliptic curve give rise to cyclic groups. This question is part of a broad theme of investigations about the distribution of Frobenius in an infinite family of division fields defined by an elliptic curve over a global field (or in variations of such families in other arithm...
متن کاملElliptic Curves, Primality Proving and Some Titanic Primes
We describe how to generate large primes using the primality proving algorithm of Atkin. Figure 1: The Titanic .
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.01.009