| Language |
English
|
| From |
2010/12/17 10:30
|
| To |
2010/12/17 12:00
|
| Place | Room 152, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | Algebra Geometrical Seminar |
| Title |
Amicable Pairs and Aliquot Cycles for Elliptic Curves |
| Field |
Algebra
Geometry
|
| Speakers | Joseph H. Silverman |
| Affiliation | Brown |
| Abstract | Let E/Q be an elliptic curve. A pair of primes (p,q) is called an amicable pair for E if #E(F_p) = q and #E(F_q) = p. More generally, an elliptic aliquot cycle is a list of primes (p_1,...,p_n) satisfying an analogous condition. In this talk I will discuss properties of elliptic amicable pairs and aliquot cycles and explain how they appear in the study of elliptic divisibility sequences. In particular, I will explain why the CM and non-CM cases are strikingly different, and will discuss in detail the strange case of j=0, whose resolution required counting points over finite fields on certain curves of genus 4. This material is joint work with Katherine Stange. |
| Link | http://www.math.kyoto-u.ac.jp/~mhyo/agsem/agseminar.html |
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