# Workshop on the ramification theory for varieties over a local field II

9-10 February 2022, online workshop

In these series of workshops, we aim to study the conductor formula for constructible sheaves on regular schemes over a local ring.

## Organizers

Fangzhou Jin, Peng Sun, Enlin Yang, Yigeng Zhao

This workshop is supported by the National Key Research and Development Program of China Grant Nr.2021YFA1001400 and the NSFC Grant Nr.12271006.

## Speakers

Xiaowen Hu

Fangzhou Jin

Peng Sun

Enlin Yang

Yigeng Zhao

## Schedule

Tencent Meeting: 777-5318-1470 pw: 235711

February 9

09:00-10:00 Log blow-up and log product 1 (Hu)

10:15-11:15 Log blow-up and log product 2 (Hu)

13:00-14:00 Lefschetz trace formula for open varieties 1 (Jin)

14:15-15:15 Lefschetz trace formula for open varieties 2 (Jin)

15:30-16:30 Intersection product with log diagonal 1 (Yang)

16:45-17:45 Intersection product with log diagonal 1 (Yang)

February 10

09:00-10:00 Brauer theory and Euler-Poincare characteristic 1 (Zhao)

10:15-11:15 Brauer theory and Euler-Poincare characteristic 2 (Zhao)

13:00-14:00 Swan class and Euler characteristic 1 (Sun)

14:15-15:15 Swan class and Euler characteristic 2 (Sun)

References:

[1] L. Illusie, Theorie de Brauer et caracteristique d'Euler-Poincare d'apres P.Deligne, Asterisque, 82-83 (1981):161-172.

[2] S. Bloch, Cycles on arithmetic schemes and Euler characteristics of curves, Proc. Sympos. Pure Math. 46 (1987):421-450.

[3] K.Kato and T.Saito, On the conductor formula of Bloch, Publ.Math.IHES, 100(2005):5-151.

[4] K.Kato and T. Saito, Ramification theory for varieties over a perfect field, Annals of Mathematics, 168(2008):33-96.