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Reduction of homomorphisms mod p and algebraicity |
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| Authors: | Chandrashekhar Khare Dipendra Prasad |
| Affiliation: | a Department of Math, University of Utah, 155 S 1400 E, Salt Lake City, UT 84112, USA b School of Mathematics, Tata Institute of Fundamental Research, Colaba, Bombay 400005, India c Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad 211019, India |
| Abstract: | Let A be an abelian variety over a number field K. Let φ 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. |
| Keywords: | Abelian variety Reduction of abelian variety Kummer theory Algebraicity |
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