School on Motives and Stacks

There will be three lecture courses - see below. In addition we will have time for exercises, question and answer sessions, discussions and some short bootcamp-talks.

The first bootcamp talk on Motives will be given by Maria Yakerson

Extra tutorial sessions will be decided upon request during the school.

All talks take place in room WSC-N-U-3.05 on the 3rd floor in the department

Preliminary Schedule

Monday Tuesday Wednesday Thursday Friday
9:00 - 10:30 Østvær Østvær Østvær Rydh
Coffee Coffee Coffee Coffee
11:00 - 12:30 Hoskins Hoskins Hoskins Østvær
Registration Lunch Lunch Lunch Lunch
14:00 - 15:30 Yakerson Q&A / Exercises Q&A / Exercises Q&A / Exercises
Coffee Coffee Coffee Coffee
16:00 - 17:30 Rydh Rydh Rydh Rydh

Mini-courses

Victoria Hoskins: Voevodsky motives of moduli stacks

Paul Arne Østvær: Equivariant motivic homotopy theory

Lecture notes for the first lecture

Lecture notes for the second lecture

Lecture notes for the third lecture

Lecture notes for the fourth lecture

David Rydh: Local structure of algebraic stacks

The nicest and easiest stacks are quotient stacks. The local structure theorem of stacks [AHR1, AHR2, AHHR3] says that every stack is étale-locally a quotient stack around a point with linearly reductive stabilizer. I will discuss the proof and some of the techniques used (deformation theory, coherent completion, Tannaka duality, Artin algebraization). Finally, I will present some applications to equivariant geometry, moduli and derived categories.

Plan of the lectures:

  • Lecture 1: Quotient stacks and good moduli spaces
  • Lecture 2: Local structure of stacks
  • Lecture 3: Deformation theory and coherent completion
  • Lecture 4: Tannaka duality, Artin approximation and equivariant Artin algebraization
  • Lecture 5: Applications
Lecture notes, exercises and references