Minimal isogeny between Drinfel'd modules

Authors
Citation
S. David et L. Denis, Minimal isogeny between Drinfel'd modules, MATH ANNAL, 315(1), 1999, pp. 97-140
Citations number
27
Categorie Soggetti
Mathematics
Journal title
MATHEMATISCHE ANNALEN
ISSN journal
00255831 → ACNP
Volume
315
Issue
1
Year of publication
1999
Pages
97 - 140
Database
ISI
SICI code
0025-5831(199909)315:1<97:MIBDM>2.0.ZU;2-K
Abstract
We give a bound for the degree of a minimal isogeny between two Drinfel'd m odules. This result is an anlogue of a theorem first proved on elliptic cur ves and then extended to abelian varieties by Masser and Wustholz. This upp er bound, as in the abelian case depends only on the height of one of the m odules and on the degree of a field over which both modules are defined. We get a polynomial bound.