View : 22 Download: 4

Explicit isogeny theorems for drinfeld modules

Title
Explicit isogeny theorems for drinfeld modules
Authors
Chen I.Lee Y.
Ewha Authors
이윤진
SCOPUS Author ID
이윤진scopus
Issue Date
2013
Journal Title
Pacific Journal of Mathematics
ISSN
0030-8730JCR Link
Citation
vol. 263, no. 1, pp. 87 - 116
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
Let F = Fq (T) and A = Fq(T) Given two nonisogenous rank-r Drinfeld A-modules φ and φ' over K, where K is a finite extension of F, we obtain a partially explicit upper bound (dependent only on φ and φ') on the degree of primes p of K such that Ppφ ≠ Ppφ', where Pp(*) denotes the characteristic polynomial of Frobenius at p on a Tate module of *. The bounds are completely explicit in terms of the defining coefficients of φ and φ', except for one term, which can be made explicit in the case of r = 2. An ingredient in the proof of the partially explicit isogeny theorem for general rank is an explicit bound for the different divisor of torsion fields of Drinfeld modules, which detects primes of potentially good reduction. Our results are a Drinfeld module analogue of Serre's work (1981), but the results we obtain are unconditional because the generalized Riemann hypothesis holds for function fields. © 2013 Mathematical Sciences.
DOI
10.2140/pjm.2013.263.87
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
Files in This Item:
001.pdf(420.17 kB)Download
Export
RIS (EndNote)
XLS (Excel)
XML


qrcode

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

BROWSE