Reduction of homomorphisms mod p and algebraicity

Khare, Chandrashekhar ; Prasad, Dipendra (2004) Reduction of homomorphisms mod p and algebraicity Journal of Number Theory, 105 (2). pp. 322-332. ISSN 0022-314X

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Let A be an abelian variety over a number field K. Let ψ be an endomorphism of A(K) into itself which reduces modulo v for almost all finite places v of K. The question we discuss in this paper is whether φ arises from an endomorphism of the abelian variety A. We answer this question in the affirmative for many cases. The question is inspired by a work of C. Corrales and R. Schoof, and uses a recent work of Larsen. We also look at the analogue of this question for linear algebraic groups.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Abelian variety; Reduction of abelian variety; Kummer theory; Algebraicity
ID Code:35692
Deposited On:12 Apr 2011 09:04
Last Modified:17 May 2016 18:39

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