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Mathematics > Number Theory

arXiv:1805.05386 (math)
[Submitted on 14 May 2018 (v1), last revised 30 Jan 2019 (this version, v2)]

Title:The de Rham isomorphism for Drinfeld modules over Tate algebras

Authors:Oğuz Gezmiş, Matthew A. Papanikolas
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Abstract:Introduced by Anglès, Pellarin, and Tavares Ribeiro, Drinfeld modules over Tate algebras are closely connected to Anderson log-algebraicity identities, Pellarin $L$-series, and Taelman class modules. In the present paper we define the de Rham map for Drinfeld modules over Tate algebras, and we prove that it is an isomorphism under natural hypotheses. As part of this investigation we determine further criteria for the uniformizability and rigid analytic triviality of Drinfeld modules over Tate algebras.
Comments: 33 pages
Subjects: Number Theory (math.NT)
MSC classes: 11G09 (Primary), 11R58, 12H10, 12J27, 14F40 (Secondary)
Cite as: arXiv:1805.05386 [math.NT]
  (or arXiv:1805.05386v2 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1805.05386
Journal reference: J. Algebra 525 (2019), 454-496
Related DOI: https://doi.org/10.1016/j.jalgebra.2019.02.006

Submission history

From: Matthew A. Papanikolas [view email]
[v1] Mon, 14 May 2018 19:10:57 UTC (34 KB)
[v2] Wed, 30 Jan 2019 23:37:41 UTC (35 KB)
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