Galois structure and de Rham invariants of elliptic curves
نویسندگان
چکیده
منابع مشابه
ON THE DE RHAM AND p-ADIC REALIZATIONS OF THE ELLIPTIC POLYLOGARITHM FOR CM ELLIPTIC CURVES
In this paper, we give an explicit description of the de Rham and p-adic polylogarithms for elliptic curves using the Kronecker theta function. We prove in particular that when the elliptic curve has complex multiplication and good reduction at p, then the specializations to torsion points of the p-adic elliptic polylogarithm are related to p-adic Eisenstein-Kronecker numbers, proving a p-adic ...
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An elliptic curve over a field K is a projective nonsingular genus 1 curve E over K along with a chosen K-rational point O of E, which automatically becomes an algebraic group with identity O. If K has characteristic 0, the n-torsion of E, denoted E[n], is isomorphic to (Z/nZ) over K. The absolute Galois group GK acts on these points as a group automorphism, hence it acts on the inverse limit l...
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The de Rham curves are a set of fairly generic fractal curves exhibiting dyadic symmetry. Described by Georges de Rham in 1957[3], this set includes a number of the famous classical fractals, including the Koch snowflake, the Peano spacefilling curve, the Cesàro-Faber curves, the Takagi-Landsberg[4] or blancmange curve, and the Lévy C-curve. This paper gives a brief review of the construction o...
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Galois representations ρ : GQ → GL2(Z/n) with cyclotomic determinant all arise from the n-torsion of elliptic curves for n = 2, 3, 5. For n = 4, we show the existence of more than a million such representations which are surjective and do not arise from any elliptic curve.
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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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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2008.09.002