Motives in May

Organized by Jake Huryn and William C. Newman.

The goal of this minicourse is to learn something about Voevodsky's triangulated category of mixed motives, with the hope of seeing some ideas from the proof of the Milnor conjecture. We plan to mainly read the book Lecture Notes on Motivic Cohomology by Mazza–Voevodsky–Weibel, which is abbreviated "MVW" below. Our reference for the proof of the Milnor conjecture will be the paper Motivic Cohomology with Z/2-coefficients by Voevodsky.

Notes from pretalks (in progress; version of 4/26)

Pretalks

Advertisement (Jake): April 11, in coordination with OSU TAGSS
Chow groups (Jake): April 15. Exercises
Sites (Jake): April 22. Exercises
Cohomology theories (Will): April 25. Exercises
Triangulated categories (Will): April 29. Exercises
Pure motives (Jake): April 30. Exercises

Talks

All talks will take place 11:00–12:30 in CH228 on M/W/F, unless otherwise stated.

Presheaves with transfers (MVW Lectures 1–2) (Will): May 2.
Homotopy invariance and motivic cohomology (MVW Lectures 2–3) (Jake): May 5.
Milnor K-theory (MVW Lecture 5) (Will): May 7.
Sheaves with transfers (MVW Lectures 6 and 13) (Will): May 9.
Triangulated categories of mixed motives (MVW Lectures 14, 8, and 9) (Jake): May 12.
Triangulated categories of mixed motives II (MVW Lecture 14) (Jake and Will): May 14.
Milnor Conjecture I (Jake): May 16.
Triangulated categories of mixed motives III (MVW Lectures 15–16) (Will): May 19 (Monday)
Milnor conjecture II (Jake): May 21 (Wednesday)
??? (Will): May 23 (Friday)
??? (???): May 26 (Monday)

The exercises for the MVW talks are to read and try to understand the material and think about the exercises from the book. We may write some notes to clarify discussion from the book and provide additional exercises. (No promises!)