The isogeny conjecture for <Emphasis Type="Italic">A</Emphasis>-motives |
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Authors: | Email author" target="_blank">Richard?PinkEmail author |
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Institution: | 1.Department of Mathematics,ETH Zurich,Zurich,Switzerland |
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Abstract: | We prove the isogeny conjecture for A-motives over finitely generated fields K of transcendence degree ≤1. This conjecture says that for any semisimple A-motive M over K, there exist only finitely many isomorphism classes of A-motives M′ over K for which there exists a separable isogeny M′→M. The result is in precise analogy to known results for abelian varieties and for Drinfeld modules and will have strong consequences for the \mathfrak p{\mathfrak {p}}-adic and adelic Galois representations associated to M. The method makes essential use of the Harder–Narasimhan filtration for locally free coherent sheaves on an algebraic curve. |
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