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The isogeny conjecture for t-motives associated to direct sums of Drinfeld modules
Authors:Richard Pink  Matthias Traulsen
Institution:Department of Mathematics, ETH Zentrum, 8092 Zurich, Switzerland
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 MM 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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