﻿ Motivic Cohomology-求真书院

### Motivic Cohomology

要：

Motivic cohomology, originated from Deligne, Beilinson and Lichtenbaum and developed by Voevodsky, is a kind of cohomology theory on schemes. It admits comparison with étale cohomology of powers of roots of unity (Beilinson-Lichtenbaum), together with higher Chow groups, and relates to K-theory by Atiyah-Hirzebruch spectral sequence. In this lecture, we establish the category of motives in which the motivic cohomologies are realized. We explain its relationship with Milnor K-theory and Chow group. Furthermore, we introduce devices like MV-sequence, Gysin triangle, projective bundle formula and duality.

Basic algebraic geometry (GTM 52, Chapter 1-3)

C. Mazza, V. Voevodsky, C. Weibel, Lecture Notes on Motivic Cohomology, American Mathematical Society, Providence, RI, for the Clay Mathematics Institute, Cambridge, MA (2006).

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• ### Quadratic conductor formulas for motivic spectra

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