Motivic Cohomology of Carlitz Twists and Its Relation to Zeta Values and Polylogarithms
Explore the fascinating world of Drinfeld modules and their significance in function field arithmetic through this comprehensive lecture. Delve into the theory of moduli and shtukas, understanding their pivotal role in the Langlands correspondence for reductive groups over function fields. Discover the parallels between Drinfeld modules and abelian varieties, examining concepts such as zeta values, Tate modules, and transcendental periods. Investigate Anderson's interpretation of shtukas as motives and learn about t-motivic cohomology, the counterpart to classical motivic cohomology. Focus on recent computations involving Carlitz twists, drawing connections to function field zeta values and polylogarithms. Gain insights into this collaborative research with A. Maurischat, expanding your knowledge of advanced mathematical concepts in number theory and arithmetic geometry.