Geodesic
Fields with vanishing $K_2$. Torsion in~$H^1(X,K_2)$ and $Ch^2(X)$
Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 108-118

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

This paper describes fields $F$ of nonzero characteristic with the property that for all finite extensions $E/F$ $K_2E=0$. We consider a somewhat wider class of fields which includes finite and separably closed fields. For smooth projective varieties $X$ over such a field we show that the groups $H^1(X,K_2)\{l\}$ and $H^2(X_{et},\mathbf Q_l|\mathbf Z_l(2))$, $NH^3(X_{et},\mathbf Q_l|\mathbf Z_l(2))$ and $Ch^2(X)\{l\}$ are isomorphic. These results are applied to describe the groups $SK_1$ of a smooth affine curve over such a field. 
@article{ZNSL_1982_116_a11,
     author = {I. A. Panin},
     title = {Fields with vanishing $K_2$. {Torsion} in~$H^1(X,K_2)$ and $Ch^2(X)$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {108--118},
     publisher = {mathdoc},
     volume = {116},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a11/}
}
TY  - JOUR
AU  - I. A. Panin
TI  - Fields with vanishing $K_2$. Torsion in~$H^1(X,K_2)$ and $Ch^2(X)$
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1982
SP  - 108
EP  - 118
VL  - 116
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a11/
LA  - ru
ID  - ZNSL_1982_116_a11
ER  - 
%0 Journal Article
%A I. A. Panin
%T Fields with vanishing $K_2$. Torsion in~$H^1(X,K_2)$ and $Ch^2(X)$
%J Zapiski Nauchnykh Seminarov POMI
%D 1982
%P 108-118
%V 116
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a11/
%G ru
%F ZNSL_1982_116_a11
I. A. Panin. Fields with vanishing $K_2$. Torsion in~$H^1(X,K_2)$ and $Ch^2(X)$. Zapiski Nauchnykh Seminarov POMI, Integral lattices and finite linear groups, Tome 116 (1982), pp. 108-118. http://geodesic.mathdoc.fr/item/ZNSL_1982_116_a11/