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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Second Lecture on the Carlitz Module

Welcome back! Here is the follow-up lecture to Tim’s introduction of the Carlitz module, this time in crisp, clear high-definition. In this second video I attempt to guide the viewer to the discovery of the Carlitz module map by following Euler’s classical calculation of the Riemann zeta values at the even integers. I would love any feedback you might have. Please let us know what you think so far by leaving a comment below. Enjoy.