Algebraic groups associated with abelian varieties
type: Item
instance of: scholarly article
title: Algebraic groups associated with abelian varieties
zbMATH Open document ID: 0697.14031
DOI: 10.1007/BF01446564
author: Takashi Ichikawa
published in: Mathematische Annalen
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164773
review text: The author extends the known results of Tankeev, Ribet, and the author on the Hodge groups and Hodge cycles of simple abelian varieties (over the field of complex numbers) to the case of non-simple abelian varieties. Especially, he shows that all Hodge cycles on non-simple abelian varieties (containing simple factors of type I, II, III, and IV) are generated by Hodge cycles of degree \( 2\) and canonical Hodge cycles constructed by Murty, under certain condition on the dimensions of those simple factors. Moreover, he shows similar results on the Zariski closures of the \(\ell\)-adic Galois groups with respect to the \(\ell\)-adic Tate modules of abelian varieties over \(\ell\)-adic local fields.
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 14G20
zbMATH DE Number: 4142208
zbMATH Keywords: Hodge groups
zbMATH Keywords: Hodge cycles
zbMATH Keywords: non-simple abelian varieties
zbMATH Keywords: \(\ell -adic\) Tate modules of abelian varieties over \(\ell \)-adic local fields
MaRDI profile type: Publication
cites work: Q5607044
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description: scientific article; zbMATH DE number 4142208