Geodesic
The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 113-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In the present paper, we introduce a category $Wor$, whose objects are affine smooth varieties over a field $k$ and morphisms are a certain variant of finite correspondences. A presheaf of abelian groups with Witt-transfers is by definition a presheaf of abelian groups on the category $Wor$. We prove the homotopy invariance of the Nisnevich sheaf associated with an arbitrary homotopy invariant presheaf with Witt-transfers. To construct a category of Witt-motives one should prove the homotopy invariance of Nisnevich cohomology of an arbitrary homotopy invariant Nisnevich sheaf with Witt-transfers. 
@article{ZNSL_2014_423_a5,
     author = {A. E. Druzhinin},
     title = {The maintenance of homotopy invariance for presheaves with {Witt-transfers} under {Nisnevich} sheafication},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {113--125},
     year = {2014},
     volume = {423},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/}
}
TY  - JOUR
AU  - A. E. Druzhinin
TI  - The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 113
EP  - 125
VL  - 423
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/
LA  - ru
ID  - ZNSL_2014_423_a5
ER  - 
%0 Journal Article
%A A. E. Druzhinin
%T The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 113-125
%V 423
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/
%G ru
%F ZNSL_2014_423_a5
A. E. Druzhinin. The maintenance of homotopy invariance for presheaves with Witt-transfers under Nisnevich sheafication. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 113-125. http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a5/

[1] V. Voevodsky, “Triangulated Category of Motives over a field”, Cycles, Transfers and Motivic Homology Theories, Annals of Math. Studies, 143, eds. V. Voevodsky, A. Suslin, E. Friedlander, 2000, 188–238 | MR | Zbl

[2] P. Balmer, “Witt groups”, Handbook of $\mathrm K$-theory, v. 2, Springer, Berlin, 2005, 539–576 | DOI | MR

[3] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, 52, Springer, 1977 | DOI | MR | Zbl

[4] M. Ojanguren, I. Panin, “A purity theorem for the Witt group”, Ann. Sci. Ecole Norm. Sup. (4), 32:1 (1999), 71–86 | MR | Zbl

[5] A. Altman, S. Kleiman, Introduction to Grothendieck Duality Theory, Lecture Notes in Mathematics, 146, Springer, 1970 | MR

[6] A. Druzhinin, Sokhranenie gomotopicheskoi invariantnosti predpuchkov s $\mathrm{Witt}$-transferami pri puchkovanii v topologii Zariskogo, Preprint 7/2014, POMI

[7] A. Druzhinin, Sokhranenie gomotopicheskoi invariantnosti predpuchkov s $\mathrm{Witt}$-transferami pri puchkovanii vtopologii Zariskogo, Preprint 8/2014, POMI

[8] K. Chepurkin, Nekotorye svoistva gomotopicheski invariantnykh predpuchkov s Vitt-transferami, Diplomnaya rabota, iyun 2013