A note on the Mumford-Tate Conjecture for CM abelian varieties
Chia-Fu Yu
TL;DR
This paper provides a new proof of the Mumford-Tate conjecture for CM abelian varieties and extends the result to CM motives, contributing to the understanding of their algebraic and Hodge-theoretic properties.
Contribution
It offers an alternative proof of the Mumford-Tate conjecture for CM abelian varieties and generalizes the result to CM motives.
Findings
New proof of the Mumford-Tate conjecture for CM abelian varieties
Extension of the conjecture's proof to CM motives
Enhanced understanding of the algebraic structures of CM motives
Abstract
The Mumford-Tate conjecture is first proved for CM abelian varieties by H. Pohlmann [Ann. Math., 1968]. In this note we give another proof of this result and extend it to CM motives.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications