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Texas A&M Number Theory Seminar

Department of Mathematics
Blocker 220
Wednesdays, 1:45–2:45 PM

Oguz Gezmis

Texas A&M University

Wednesday, September 27, 2017

Blocker 220, 1:45PM

Title: De Rham isomorphism for Drinfeld modules over Tate algebras

Abstract: Two main concepts of the arithmetic on function fields are elliptic (Drinfeld) modules and L-Series. On 1970's, Drinfeld introduced elliptic modules which can be seen as an analogue of elliptic curves in function field setting and D. Goss introduced a new type of L-Series as an anologue of Rieamann Zeta Function. In 2012, Pellarin defined an L-series in Tate algebras which is a deformation of Goss's L-series. In order to give new identities for Pellarin L-Series, Angles, Pellarin and Tavares Ribeiro introduced Drinfeld modules over Tate algebras. In this talk, we talk about Drinfeld modules over Tate algebras of arbitrary rank. We also prove De Rham isomorphism for these modules under some conditions. Finally, we prove Legendre's Relation under this new setting. This is joint work with Matthew A. Papanikolas.