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Uniformizable families of $ t$-motives


Authors: Gebhard Böckle and Urs Hartl
Journal: Trans. Amer. Math. Soc. 359 (2007), 3933-3972
MSC (2000): Primary 11G09; Secondary 14G22
DOI: https://doi.org/10.1090/S0002-9947-07-04136-0
Published electronically: February 23, 2007
MathSciNet review: 2302519
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Abstract: Abelian $ t$-modules and the dual notion of $ t$-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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Additional Information

Gebhard Böckle
Affiliation: Institut für Experimentelle Mathematik, Universität Duisburg-Essen, Campus Essen, Ellernstr. 29, D–45326 Essen, Germany
Email: boeckle@iem.uni-due.de

Urs Hartl
Affiliation: Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstr. 1, D – 79104 Freiburg, Germany

DOI: https://doi.org/10.1090/S0002-9947-07-04136-0
Keywords: Drinfeld modules, higher dimensional motives, rigid analytic geometry
Received by editor(s): November 15, 2004
Received by editor(s) in revised form: July 21, 2005
Published electronically: February 23, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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