A hermitian analogue of the Broecker-Prestel theorem

The Broecker-Prestel local-global principle characterizes weak isotropy of quadratic forms over a formally real field in terms of weak isotropy over the henselizations and isotropy over the real closures of that field. A hermitian analogue of this principle is presented for algebras of index at most two. An improved result is also presented for algebras with a decomposable involution, algebras of pythagorean index at most two, and algebras over SAP and ED fields.Comment: Final pre-publication versio

Hermitian Sylvester and Pfister theorems for Azumaya algebras with involution

We investigate connections between a pairing of hermitian forms extensively studied by Garrel, signatures of hermitian forms, and positive semidefinite quadratic forms, and use them to prove a version of Sylvester's law of inertia as well as Pfister's local-global principle for hermitian forms over Azumaya algebras with involution over semilocal rings.Comment: 29 page

Signatures of hermitian forms and the Knebusch Trace Formula

Signatures of quadratic forms have been generalized to hermitian forms over algebras with involution. In the literature this is done via Morita theory, which causes sign ambiguities in certain cases. In this paper, a hermitian version of the Knebusch Trace Formula is established and used as a main tool to resolve these ambiguities. The last page is an erratum for the published version. We inadvertently (I) gave an incorrect definition of adjoint involutions; (II) omitted dealing with the case $(H\times H, \widehat{\phantom{m}}\,)$. As $W(H\times H, \widehat{\phantom{m}}\,)= W(R\times R, \widehat{\phantom{m}}\,)=0$, the omission does not affect our reasoning or our results. For the sake of completeness we point out where some small changes should be made in the published version.Comment: This is the final version before publication. The last page is an updated erratum for the published versio

CFHTLS weak-lensing constraints on the neutrino masses

We use measurements of cosmic shear from CFHTLS, combined with WMAP-5 cosmic microwave background anisotropy data, baryonic acoustic oscillations from SDSS and 2dFGRS and supernovae data from SNLS and Gold-set, to constrain the neutrino mass. We obtain a 95% confidence level upper limit of 0.54 eV for the sum of the neutrino masses, and a lower limit of 0.03 eV. The preference for massive neutrinos vanishes when shear-measurement systematics are included in the analysis.Comment: 10 pages. Published versio