Number Theory Seminar

Date: September 27, 2017

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: Oguz Gezmis, Texas A&M University

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.

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