HENSELIAN VALUATIONS OF DIVISION RINGS AND THE GROUPSK₁

Abstract

We study collisions between rare-gas atoms in the 3Pz metastable state and in the ground state. We create the metastable atoms by a discharge, orient them by optical pumping and measure the pressure broadening of their magnetic-resonance curves. For xenon, we use mixtures of even and odd isotopes; this leads to a determination of the cross section for metastability-exchange collisions. For krypton, we report results for the disorientation of the metastable state in the natural gas. In addition, we have measured the disorientation cross section of the krypton metastable state through collisions with helium.

Reduced K-theory of Azumaya algebras

“…It seems that in the above example the condition char F i(D) is not necessary. This suggest that there might be a weaker condition for being tame as it is available for valued division algebras observed by Ershov in [4].…”

Galois cohomology and forms of algebras over Laurent polynomial rings

“…8 So v A is a valuation. The formula v A = 1 n v • N was proven independently by Ershov [17,18] and Wadsworth [49]. …”

On the First Galois Cohomology Group of the Algebraic Group SL1(D)

“…Now let m = index D and m = Z D F . Following Ershov (1983) define a valuation on D to be tame if Z D is a separable extension over F and char F l where l = n/mm . If D is of this nature, then we have…”