Lower bounds for ranks of Mumford-Tate groups
File(s)
Accepted version
Author(s)
Orr, M
Type
Journal Article
Abstract
Let A be a complex abelian variety and G its Mumford--Tate group. Supposing that the simple abelian subvarieties of A are pairwise non-isogenous, we find a lower bound for the rank of G, which is a little less than log_2 dim A. If we suppose that End A is commutative, then we show that rk G >= log_2 dim A + 2, and this latter bound is sharp. We also obtain the same results for the rank of the l-adic monodromy group of an abelian variety defined over a number field.
Date Issued
2015-05-01
Date Acceptance
2013-06-21
Citation
Bulletin de la Societe Mathematique de France, 2015, 143 (2), pp.229-246
ISSN
0037-9484
Start Page
229
End Page
246
Journal / Book Title
Bulletin de la Societe Mathematique de France
Volume
143
Issue
2
Copyright Statement
© Société Mathématique de France
Subjects
General Mathematics
0101 Pure Mathematics
Publication Status
Published