Speaker: Ren Fei, University of Wuppertal

Date: October 9, 2025

Time: 14:00-15:00 pm

Location: B1032, Zhixin Building, Shandong University

Sponsor: School of Mathematics, Shandong University

Abstract:

Let X be a smooth proper scheme over a perfect field k of positive characteristic p. For p-primary torsion sheaves on X, there are two duality theories which are fundamentally different: one is the Serre-Grothendieck duality for coherent sheaves on X, which is later generalized by Ekedahl to a duality theory for coherent sheaves on W_nX with the top dRW sheaf being the dualizing sheaf; the other one is the Milnor-Kato-duality, which works for a much bigger class of sheaves, and has the top log dRW sheaf as the dualizing sheaf. The basis of Ekedahl's work is that regular dRW differentials admit a perfect pairing via the wedge product, just as regular Kähler differentials under the Serre-Grothendieck duality. Then it is natural to ask:

1. What if we allow the differentials to have certain poles along a divisor D, do we still get a good duality theory?

2. What should be the natural definition for a "dRW sheaf with ramification along D"?

3. What is the dual of a given ramified dRW sheaf, can it also be defined naturally? Can one say something about its structure?

In this talk, we will discuss our solutions to these questions, and how our ramified duality theory extends to a ramified version of the Milne-Kato duality. On the side of zeros in terms of Milnor-Kato, we give an explicit description of the structure of our motivic complex.

Part of this talk is based on joint work with Kay Rüling.

For more information, please visit:

https://www.view.sdu.edu.cn/info/1020/206539.htm