The isogeny conjecture for t-motives associated to direct sums of Drinfeld modules Original Research Article

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 image, 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 image. 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 image.