99 research outputs found
Prime divisors of sequences associated to elliptic curves
We consider the primes which divide the denominator of the x-coordinate of a
sequence of rational points on an elliptic curve. It is expected that for every
sufficiently large value of the index, each term should be divisible by a
primitive prime divisor, one that has not appeared in any earlier term. Proofs
of this are known in only a few cases. Weaker results in the general direction
are given, using a strong form of Siegel's Theorem and some congruence
arguments. Our main result is applied to the study of prime divisors of Somos
sequences
Periodic points for good reduction maps on curves
The periodic points of a morphism of good reduction for a smooth projective
curve with good reduction over the p-adics form a discrete set. This is used to
give an interpretation of the morphic height in terms of asymptotic properties
of periodic points, and a morphic analogue of Jensen's formula
Explicit local heights
A new proof is given for the explicit formulae for the non-archimedean
canonical height on an elliptic curve. This arises as a direct calculation of
the Haar integral in the elliptic Jensen formula
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