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$G$-torsor over $\mathbb{A}^1_S$ where characteristic of $S$ does not divide $|G|$

I am reading the paper $\mathbb{A}^1$-homotopy theory of schemes by Morel and Voevodsky from 1999. There is a proposition saying that Let $G$ be a finite étale group scheme over $S$ of order prime to …
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157 views

A fibration is a map which has the right lifting property with respect to injections that ar...

As mentioned in Motivic Homotopy Theory, an alternative criterion for $X\rightarrow Y$ to be a fibration is that the diagram $$\require{AMScd} \begin{CD} A @>>> X;\\ @VV{i}V @VVV \\ B @>>> Y; \end{CD} …