Variation of the canonical height for a family of polynomials

Details Variation of the canonical height for a family of polynomials Variation of the canonical height for a family of polynomials

2010-03-22

arxiv.org/abs/1003.4225v3

Mathematics

Number Theory

23 pages; a few minor changes made since first version (the previous update attempt failed to actually update the paper)

Scientific paper

A theorem of Tate asserts that, for an elliptic surface E/X defined over a number field k, and a section P of E, there exists a divisor D on X such that the canonical height of the specialization of P to the fibre above t differs from the height of t relative to D by at most a bounded amount. We prove the analogous statement for a one-parameter family of polynomial dynamical systems. Moreover, we compare, at each place of k, the local canonical height with the local contribution to the height relative to D, and show that the difference is analytic near the support of D, a result which is analogous to results of Silverman in the elliptic surface context.

Affiliated with

Also associated with

No associations

Rating

Variation of the canonical height for a family of polynomials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Variation of the canonical height for a family of polynomials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Variation of the canonical height for a family of polynomials will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206959