Andrei Druzhinin
Published 2017-09-19Version 1
The category of effective Grothendick-Witt-motives (and Witt-motives) of smooth varieties in a similar way as Voevodsky category of motives $DM^-_{eff}(k)$, starting with some category of GW-correspondences (and Witt-correspondences) over a perfect field $k$, $char\,k\neq 2$, is defined. The functor $M^{GW}_{eff}\colon Sm_k\to DM^{GW}_{eff}(k)$ of Grothendick-Witt-motives of smooth varieties is computed and it is proved that for any smooth variety $X$ and homotopy invariant sheave with GW-transfers $\cal F$ $$ Hom_{DM^{GW}_{eff}(k)}(M^{GW}_{eff}(X), \mathcal F[i]) \simeq H^i_{Nis}(X,\mathcal F) $$ naturally in $X$ and $\cal F$.
Comments: arXiv admin note: text overlap with arXiv:1601.05383
The deformation theory of representations of the fundamental group of a smooth variety
On the center of the ring of differential operators on a smooth variety over $\bZ/p^n\bZ$
Chern Numbers of Smooth Varieties via Homotopy Continuation and Intersection Theory
![QR code for arXiv:1709.06273 [math.AG]](http://oss.arxitics.com/images/favicon.svg)