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ISSN 1088-6850(e) ISSN 0002-9947(p)

Uniformizable families of -motives

Author(s): Gebhard Böckle; Urs Hartl
Journal: Trans. Amer. Math. Soc. 359 (2007), 3933-3972.
MSC (2000): Primary 11G09; Secondary 14G22
Posted: February 23, 2007
MathSciNet review: 2302519
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Abstract: Abelian -modules and the dual notion of -motives were introduced by Anderson as a generalization of Drinfeld modules. For such Anderson defined and studied the important concept of uniformizability. It is an interesting question and the main objective of the present article to see how uniformizability behaves in families. Since uniformizability is an analytic notion, we have to work with families over a rigid analytic base. We provide many basic results, and in fact a large part of this article concentrates on laying foundations for studying the above question. Building on these, we obtain a generalization of a uniformizability criterion of Anderson and, among other things, we establish that the locus of uniformizability is Berkovich open.

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