A Conjectural Reciprocity Law for Realizations of Motives
Prof. Dustin Clausen
2023-04-26 17:00-18:30
MCM110
Speaker: Prof. Dustin Clausen (IHES)Time: 17:00-18:30 April 26, 2023 (Wednesday)
Place: MCM110 (Zoom Live)
Title: A Conjectural Reciprocity Law for Realizations of Motives
Abstract: A motive over a scheme S is a bit of linear algebra which is supposed to "universally" capture the cohomology of smooth proper S-schemes. Motives can be studied via various "realizations", which are objects of more concrete linear algebraic categories attached to S. It is known that over certain S, these different realizations are related to one another via comparison isomorphisms, as in Hodge theory. In this talk, I will try to explain that for completely general S, there is a much more subtle kind of relationship between these realizations, which takes a similar form to classical reciprocity laws in number theory.
