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15 votes
3 answers
3k views

State of the art for Gersten's conjecture for K-theory?

Does anyone know (of a reference to) under what restrictions on the regular scheme $X$ it is known that we have an exact sequence $$0 \to \mathcal{K}_n(X) \to \bigoplus_{x \in X^{(0)}} K_n(k(x)) \to \...
name's user avatar
  • 1,347
3 votes
1 answer
294 views

A class in the motivic cohomology group $H^{0,1}(\operatorname{Spec}k;\mathbb{Z}/p)$

In the following paper N. Yagita, Examples for the Mod p Motivic Cohomology of Classifying Spaces, on the first page, below display (1.1), it says "It is known that there is an element $\tau\in H^...
Xing Gu's user avatar
  • 935
3 votes
0 answers
224 views

Loop spaces of motivic Eilenberg-Mac Lane spaces

Consider the unstable $\mathbb{A}^1$-homotopy category (say over $\mathbb{C}$). By the loop space $\Omega X$ of an object $X$, we mean the homotopy fiber of $pt\to X$. For an abelian group A and the ...
Xing Gu's user avatar
  • 935