Root numbers of elliptic curves in residue characteristic 2
نویسندگان
چکیده
منابع مشابه
Galois Theory, Elliptic Curves, and Root Numbers
The inverse problem of Galois theory asks whether an arbitrary finite group G can be realized as Gal(K/Q) for some Galois extension K of Q. When such a realization has been given for a particular G then a natural sequel is to find arithmetical realizations of the irreducible representations of G. One possibility is to ask for realizations in the Mordell-Weil groups of elliptic curves over Q: Gi...
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We introduce a height measure on Q to count rational numbers. Through it, we prove a density result on the average value of the root numbers of families of twists of elliptic curves. Zagier and Kramarz computed in [11] the rank of the curves x + y = m, with m an integer < 70, 000. These data suggest that the rank is even for exactly half of the twists of x + y = 1. This conjecture has been prov...
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The growth of the Mordell-Weil rank of an elliptic curve in a tower of number fields can be discussed at many levels. On the one hand, the issues raised can be embedded in a broader Iwasawa theory of elliptic curves (Mazur [10]); on the other hand, they can be crystallized in a single easily stated question, namely whether the rank of the elliptic curve over subextensions of finite degree is bo...
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This article is broadly based on the talk that was given at the symposium ‘Perspectives in the Mathematical Sciences’, held at Indian Statistical Institute (ISI), Bangalore, to celebrate the Platinum Jubilee of the ISI. I would like to thank the organisers, especially Professor N.S.N. Sastry, for inviting me to lecture on this occasion. The article is intended for a general audience and does no...
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Introduction. In [Ge1] Gekeler classified all elliptic curves over F2r (T ) with one rational place of multiplicative reduction (without loss of generality located at ∞), one further rational place of bad reduction (without loss of generality located at 0) and good reduction elsewhere. So these curves have conductor ∞ · T where n is a natural number (which actually can be arbitrarily large). In...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2008
ISSN: 0024-6093
DOI: 10.1112/blms/bdn034