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I have been trying to unravel some of the known relationships between various ideas on mixed motives. I find the literature quite hard to follow -"from experts, for experts". Voevodsky in "...

Theorem 1.2 of the paper "The motivic Hopf map solves the homotopy limit problem for K-theory" (see https://elibm.org/article/10011880) says that (under certain assumptions on the base field) the ...

Let $X$ be an integral locally noetherian smooth scheme over base field $k$. Then for every $x \in X^{(1)}$ point of codimension $1$, the stalk $\mathcal{O}_{X,x}$ is a discrete valuation ring. ...

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^...

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 ...