Geodesic
Rigidity theorem for presheaves with Witt-transfers
Algebra i analiz, Tome 31 (2019) no. 4, pp. 114-136.

Voir la notice de l'article provenant de la source Math-Net.Ru

The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field $ k$ of characteristic different form two is proved. Namely, for any such sheaf $ F$, isomorphism $ \mathcal F(U)\simeq \mathcal F(x)$ is established, where $ U$ is an essentially smooth local Henselian scheme with a separable residue field over $ k$. As a consequence, the rigidity theorem for the presheaves $ W^i(-\times Y)$ for any smooth $ Y$ over $ k$ is obtained, where the $ W^i(-)$ are derived Witt groups. Note that the result of the work is rigidity with integral coefficients. Other known results are state isomorphisms with finite coefficients.
Keywords: rigidity theorem, presheaves with transfers, Witt-correspondences. 
@article{AA_2019_31_4_a3,
     author = {A. E. Druzhinin},
     title = {Rigidity theorem for presheaves with {Witt-transfers}},
     journal = {Algebra i analiz},
     pages = {114--136},
     publisher = {mathdoc},
     volume = {31},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2019_31_4_a3/}
}
TY  - JOUR
AU  - A. E. Druzhinin
TI  - Rigidity theorem for presheaves with Witt-transfers
JO  - Algebra i analiz
PY  - 2019
SP  - 114
EP  - 136
VL  - 31
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2019_31_4_a3/
LA  - ru
ID  - AA_2019_31_4_a3
ER  - 
%0 Journal Article
%A A. E. Druzhinin
%T Rigidity theorem for presheaves with Witt-transfers
%J Algebra i analiz
%D 2019
%P 114-136
%V 31
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2019_31_4_a3/
%G ru
%F AA_2019_31_4_a3
A. E. Druzhinin. Rigidity theorem for presheaves with Witt-transfers. Algebra i analiz, Tome 31 (2019) no. 4, pp. 114-136. http://geodesic.mathdoc.fr/item/AA_2019_31_4_a3/

[1] Suslin A., “On the K-theory of algebraically closed fields”, Invent. Math., 73:2 (1983), 241–245

[2] Gabber O., “K-theory of Henselian local rings and Henselian pairs”, Contemp. Math., 126, Amer. Math. Soc., Providence, RI, 1992, 59–70

[3] Gillet H., Thomason R., “The K-theory of strict Hensel local rings and a theorem of Suslin”, J. Pure Appl. Algebra, 34:2–3 (1984), 241–254

[4] Suslin A., “On the K-theory of local fields”, J. Pure Appl. Algebra, 34:2–3 (1984), 301–318

[5] Suslin A., Voevodsky V., “Singular homology of abstract algebraic varieties”, Invent. Math., 123:1 (1996), 61–94

[6] Panin I., Yagunov S., “Rigidity for orientable functors”, J. Pure Appl. Algebra, 172:1 (2002), 49–77

[7] Hornbostel J., Yagunov S., “Rigidity for Henselian local rings and $A1$-representable theories”, Math. Z., 255:2 (2007), 437–449

[8] Yagunov S., “Rigidity. II. Non-orientable case”, Doc. Math., 9 (2004), 29–40

[9] Röndings O., Østvær P., “Rigidity in motivic homotopy theory”, Math. Ann., 341:3 (2008), 651–675

[10] Neshitov A., “Teorema zhestkosti dlya predpuchkov s $\Omega$-transferami”, Algebra i analiz, 26:6 (2014), 78–98

[11] Bachmann T., Motivic and real etale stable homotopy theory, 2016, arXiv: 1608.08855

[12] Druzhinin A., Triangulated category of effective Witt-motives $ DWM_{eff}(k)$, 2016, arXiv: 1601.05383

[13] Balmer P., “Witt cohomology, Mayer–Vietoris, homotopy invariance and the Gersten conjecture”, K-Theory, 23:1 (2001), 15–30

[14] Balmer P., “Witt groups”, Handbook of K-theory, v. 2, Springer, Berlin, 2005, 539–576

[15] Altman A., Kleiman S., Introduction to Grothendieck duality theory, Lecture Notes in Math., 146, Springer, Berlin, 1970

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

[17] Panin I., Stavrova A., Vavilov N., Grothendieck–Serre conjecture I: appendix, 2009, arXiv: 0910.5465