Abstract:

First part: Deligne--Illusie's results and applications;
We'll start from Hodge deccomposition, then talk about Deligne--Illusie's approach. Then, if time permits, Kodaira vanishing.

Second part: approximation of BG;

We shall decode the following one-paragraph-idea: one approximates B(alpha_p) to transport the non-degeneracy of the Hodge-to-de Rham spectral sequence for B(alpha_p) to that of a smooth projective variety X. A consequence is that alpha_p doesn't lift to W_2 (what an absurd proof!). 
The following topics will be lightly touched:
(1) finite flat commutative group schemes in characteristic p;
(2) classifying stack of such group schemes;
(3) (Q)Coh(BG);
(4) cotangent complex (of reasonable maps between reasonable stacks);
(5) approximations of BG.

In the highly unlikely event of having some time left, there will be the last part: Impromptu talk on the speaker's recent works, e.g.: more on cohomology of BG (Kubrak--L--Mondal, upcoming), or maybe more on the Deligne--Illusie's splitting (Drinfeld, Bhatt--Lurie, L--Mondal).

腾讯会议：

340-9786-9627

（https://meeting.tencent.com/dm/pPaUlFfwLtHN）

11/18、11/25、12/2、12/16        10:00-11:30

11/23、11/30、12/7、12/14         13:00-14:30