Hodge groups of Abelian varieties with purely multiplicative reduction

A. Silverberg, Yu G. Zarhin

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The main result of the paper is that if A is an Abelian variety over a subfield F of C, and A has purely multiplicative reduction at a discrete valuation of F, then the Hodge group of A is semisimple. Further, we give necessary and sufficient conditions for the Hodge group to be semisimple. We obtain bounds on certain torsion subgroups for Abelian varieties which do not have purely multiplicative reduction at a given discrete valuation, and so obtain bounds on torsion for Abelian varieties, defined over number fields, whose Hodge groups are not semisimple.

Original languageEnglish (US)
Pages (from-to)379-389
Number of pages11
JournalIzvestiya Mathematics
Volume60
Issue number2
DOIs
StatePublished - Dec 1 1996

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Hodge groups of Abelian varieties with purely multiplicative reduction'. Together they form a unique fingerprint.

  • Cite this