The isogeny conjecture for t-motives associated to direct sums of Drinfeld modules |
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Authors: | Richard Pink Matthias Traulsen |
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Institution: | Department of Mathematics, ETH Zentrum, 8092 Zurich, Switzerland |
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Abstract: | Let K be a finitely generated field of transcendence degree 1 over a finite field. Let M be a t-motive over K of characteristic p0, which is semisimple up to isogeny. The isogeny conjecture for M says that there are only finitely many isomorphism classes of t-motives M′ over K, for which there exists a separable isogeny M′→M of degree not divisible by p0. For the t-motive associated to a Drinfeld module this was proved by Taguchi. In this article we prove it for the t-motive associated to any direct sum of Drinfeld modules of characteristic p0≠0. |
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