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

✍ Scribed by Richard Pink; Matthias Traulsen

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
239 KB
Volume
117
Category
Article
ISSN
0022-314X

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✦ Synopsis

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 p 0 , 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 p 0 . 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 p 0 = 0.

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