Third Lecture: A Dirichlet Unit Theorem for the Carlitz Module

In this video Tim tells us about a (fairly) new (and long desired!) construction of L. Taelman of unit and class modules associated to a given Drinfeld module. In this lecture we focus on the Carlitz module and give all of the relevant definitions with (hopefully) beneficial motivational explanations. Tim begins by recalling the classical Dirichlet unit theorem for number fields in such a way as to make a tighter analogy when it comes to Taelman’s machine. Enjoy!

References for this video can be found on L. Taelman’s homepage, http://www.math.leidenuniv.nl/~lenny/. Of particular interest for us are the papers A Dirichlet unit theorem for Drinfeld modules and Arithmetic of characteristic p special L-values. Please check them out!

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