Variations on a theme of Minkowski and Serre

A. Silverberg, Yu G. Zarhin

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

If α is a root of unity in an integral domain O of characteristic zero, (α - 1 )k ∈ nO, and no prime divisor of n is a unit in O, then α = 1 if n is a positive integer outside a finite set determined by k. We prove this result and generalizations of it, and give results when n is an element of the finite exceptional set. We give applications to endomorphisms of semi-abelian varieties, compatible systems of l-adic representations, and the cohomology of projective varieties.

Original languageEnglish (US)
Pages (from-to)285-302
Number of pages18
JournalJournal of Pure and Applied Algebra
Volume111
Issue number1-3
DOIs
StatePublished - Aug 26 1996

Fingerprint

Finite Set
Exceptional Sets
Abelian Variety
Integral domain
Projective Variety
Roots of Unity
Endomorphisms
Divisor
Cohomology
Unit
Integer
Zero
Generalization

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Variations on a theme of Minkowski and Serre. / Silverberg, A.; Zarhin, Yu G.

In: Journal of Pure and Applied Algebra, Vol. 111, No. 1-3, 26.08.1996, p. 285-302.

Research output: Contribution to journalArticle

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