4
$\begingroup$

There are two ways to define Borel-Moore motivic homology (of schemes) with rational coefficients: one should either consider certain complexes of algebraic cycles, or the $\gamma$-filtrations of Quillen's K'-theory $\otimes \mathbb{Q}$. Now, I would like to treat this homology for more or less general excellent Noetherian finite-dimensional schemes. My question is: are there any papers that treat Borel-Moore motivic homology in this generality? It seems that (the newer) cycle complex approach (related with motives a-la Voevodsky) usually demands the schemes to be of finite type over Dedekind domains, whereas the best K'-theoretic source that I know is: Soule C., Operations en K-theorie algebrique// Can. J. Math. 37 (1985), 488-550

and it requires the schemes considered to be quasi-projective over regular ones. Does a more general paper on $\gamma$-filtrations exist now?

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.