About the decomposition of a Chow group of a variety Sorry; usually these filtrations are defined on $Q$-linear Chow groups only, aren't they? Then what's the point of saying that the filtration splits? Are you speaking about some canonical splitting here? Moreover, in the general case there quite natural reasons for this filtration to split (though not quite canonically).

Nov
7

comment

Lubin-Tate modules and different uniformizers If you increase the residue field then the reduction of $h\circ [\pi]_F\circ h^{-1}$ ($h$ is a "change of variables") does not have to equal $X^q$. As about $[\pi'-\pi]$: since $\pi'-\pi$ has finite valuation, some iteration of $[\pi']$ factors through $[\pi'-\pi]$.