Abstract:

Drinfeld modules over Tate algebras were constructed by Anglès, Pellarin, and Tavares Ribeiro to find ways to better interpret various objects in function field arithmetic, including Anderson log-algebraicity identities, Pellarin L-series, and Taelman class modules.  At their core Drinfeld modules over Tate algebras are rings of Frobenius difference operators acting on the Tate algebra of the closed unit polydisc over the rational function field in positive characteristic.  We will discuss the de Rham map for Drinfeld modules over Tate algebras, which arises through the study of biderivations and quasi-periodic operators, and we will show that it is an isomorphism under certain conditions.  As part of these investigations we will find criteria for the uniformizability of Drinfeld modules over Tate algebras.  Joint work with O. Gezmis.