Milnor-Witt Motives seminar

Milnor-Witt motives seminar 2023

This is a learning seminar for Milnor-Witt motives following Milnor-Witt Motives .

If you would like to participate, contact Roy Magen.
We meet 15:05-16:00 in room 528.

Applications and computations
- On the rational motivic homotopy category
- Homotopy Invariance of Nisnevich Sheaves with Milnor-Witt Transfers
- Split Milnor-Witt Motives and its Applications to Fiber Bundles
- Framed and MW-transfers for homotopy modules
- Milnor-Witt K-theory for finite fields
- Chow-Witt:
  - Chow-Witt rings of classifying spaces for symplectic and special linear groups Note proposition 3.3 gives bijection between degree i Chow-Witt group of classifying spaces and degree i characteristic classes, analogous to theorem 1.3 of Totaro's paper
  - Chow-Witt rings of Grassmannians
More reading
- Milnor K-theory of rings, higher Chow groups and applications
- Rost: Chow Groups with Coefficients
- Fasel: Lectures on Chow-Witt groups
- Niels Feld: Milnor-Witt Cycle Modules
- Morel: A1-Algebraic Topology over a Field
- Milnor: Algebraic K-Theory and Quadratic Forms

For more resources on motivic homotopy theory, see here .

Talks

Date	Speaker	Topic	Main resource(s)
February 09	Roy	Organizational meeting	Chapter 1
February 16	Morena	Milnor-Witt K-theory	Chapter 2 section 1, Milnor-Witt K-theory for finite fields
February 23	Morena, Roy	More on Milnor-Witt K-theory	Chapter 2 sections 1,2
March 2	Roy	Homotopy invariance and transfers in Milnor-Witt K-theory	Chapter 2 section 2, Milnor-Witt Cycle Modules , Lectures on Chow-Witt groups
March 9	Andres	Chow-Witt groups	Chapter 2 section 3, Fasel: Lectures on Chow-Witt groups
March 29	Andres	Chow-Witt groups	Fasel: Lectures on Chow-Witt groups
April 6	Andres	Chow-Witt groups	Fasel: Lectures on Chow-Witt groups
April 13	Roy	Finite Milnor-Witt correspondences	Chapter 2 section 4
Morena