Tom Bachmann (Uni Mainz): Filtrations and endomorphisms via stacks

Main references: [Bhatt, Section 2.2.1 and 2.2.2], [BL1, App. D], and
[Mou].
(1) Explain quotient stacks of a scheme by a functor of groups, see for instance
[Kha, Section 4.4, in particular Theorem 4.28]8.
(2) Explain the notion of a graded and a filtered derived category. Explain
completeness, canonical and stupid filtration, mention its symmetric monoidal structure without defining precisely what a symmetric monoidal
structure is9, and explain the standard and the Beilinson t-structure.
3(3) Introduce the quotient stack A1=Gm, explain that it classifies generalized
Cartier divisors, see [Bhatt, 2.2.5] or [KhRy, 3.2].
(4) Formulate and prove [Bhatt, 2.2.6 + 2.2.8].
(5) Explain Gca and V\(E) for a vector bundle E.
(6) Explain [Bhatt, 2.2.12 + 2.2.13] without going too much into detail although it would be nice to see, where \characteristic zero” is needed.
(7) If time permits, explain [Bhatt, 2.2.14 { 2.2.16].
(8) In any case, explain [Bhatt, 2.2.17].

https://tu-darmstadt.zoom.us/j/62421505417?pwd=NDhEdUJPb0RaUTNzQyt4R0U1N2lzUT09

Meeting-ID: 624 2150 5417
Kenncode: 100002