| Abstrakt: |
Let K be the fraction field of a two-dimensional henselian, excellent, and equicharacteristic local domain. We prove a local-global principle for Galois cohomology with certain finite coefficients over K. We use classical machinery from étale cohomology theory, drawing upon an idea in Saito's work on two-dimensional local class field theory. This approach works equally well over the function field of a curve over an equi-characteristic henselian discrete valuation field, thereby giving a different proof of (a slightly generalized version of) a recent result of Harbater, Hartmann, and Krashen. We also present two applications. One is the Hasse principle for torsors under quasisplit semisimple simply connected groups without E8 factor. The other gives an explicit upper bound for the Pythagoras number of a Laurent series field in three variables. This bound is sharper than earlier estimates. [ABSTRACT FROM AUTHOR] |
