Norm residue isomorphism theorem seminar

Fall 2021

The goal of this seminar is to understand (some portion of) the proof of the norm residue isomorphism theorem by Voevodsky, Rost, Suslin, Weibel, Haesemeyer, and others. Since the proof is quite complicated we will sketch some parts of the proof of the existence of Rost varieties.

Time and place

10:00-11:30 AM Tuesdays, room 622 in the math building.

References

[1] Christian Haesemeyer and Charles A Weibel. The norm residue theorem in motivic cohomology. Princeton University Press, 2019.

[2] Carlo Mazza, Vladimir Voevodsky, Charles Weibel. Lecture notes on motivic cohomology. American Mathematical Society, 2006.

[3] Alexander Merkurjev. On the norm residue homomorphism of degree two. Translations of the American Mathematical Society-Series 2, 219:103-124, 2006.

[4] Wilberd van der Kallen. The Merkurjev-Suslin theorem. In Orders and their Applications, pages 157-168. Springer, 1985.

[5] Vladimir Voevodsky. Motivic cohomology with \(\mathbb{Z}/2\)-coefficients. Publications Mathématiques de l'IHÉS, 98:59-104, 2003.

[6] Vladimir Voevodsky. On motivic cohomology with \(\mathbb{Z}/\ell\)-coefficients. Annals of Mathematics, pages 401-438, 2011.

Schedule

  Date Speaker Topic References Notes
September 21 Avi Zeff Introduction and reductions [1, §1.1-1.4], [3] PDF
September 28 Caleb Ji Motivic cohomology [2] PDF
October 5 Hung Chiang \(\mathbb A^1\)-homotopy theory, the Nisnevich topology, and the reverse induction steps [1, §2.1-2.2], [2] PDF
October 12 Hung Chiang, Avi Zeff Completion of reverse induction and cohomology of singular varieties/with supports [1, §2.3-2.4]
October 19 Haodong Yao Equivalences of conditions [TENTATIVE]
October 26 Baiqing Zhu Proof up to Rost varieties [TENTATIVE]
November 2 David Marcil The Rost motive [TENTATIVE]