The splitting of reductions of an abelian variety
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Publication:2927905
DOI10.1093/IMRN/RNT113zbMATH Open1318.14040arXiv1111.0624OpenAlexW2962762360MaRDI QIDQ2927905
Author name not available (Why is that?)
Publication date: 5 November 2014
Published in: (Search for Journal in Brave)
Abstract: Consider an absolutely simple abelian variety A defined over a number field K. For most places v of K, we study how the reduction A_v of A modulo v splits up to isogeny. Assuming the Mumford-Tate conjecture for A and possibly increasing K, we will show that A_v is isogenous to the m-th power of an absolutely simple abelian variety for all places v of K away from a set of density 0, where m is an integer depending only on the endomorphism ring End(A_Kbar). This proves many cases, and supplies justification, for a conjecture of Murty and Patankar. Under the same assumptions, we will also describe the Galois extension of Q generated by the Weil numbers of A_v for most v.
Full work available at URL: https://arxiv.org/abs/1111.0624
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