Torsion zero-cycles and the Abel-Jacobi map over the real numbers

This is a study of the torsion in the Chow group of zero-cycles on a variety over the real numbers. The first section recalls important results from the literature. The rest of the paper is devoted to the study of the AbelJacobi map a: A0XAlbXR restricted to torsion subgroups. Using Roitmans theorem over the complex numbers and a version of Blochs cohomological AbelJacobi map over the real numbers, it is shown that this map can be described completely in terms of ´etale cohomology. For some examples (products of curves, abelian varieties, certain fibre bundles) the torsion in the kernel and cokernel of the AbelJacobi map a is computed explicitly

Lichtenbaum-Tate duality for varieties over p-adic fields

S. Lichtenbaum has proved in [L1] that there is a nondegenerate pairing Pic(C)x Br(C)->Br(K) =Q/Z (1) between the Picard group and the Brauer group of a nonsingular projective curve C over a p-adic field K (a finite extension of the p-adic numbers Qp). His proof consists of a reduction via explicit cocycle calculations in Galois cohomology to a combination of Tate duality for group schemes over p-adic fields and the autoduality of the Jacobian of a smooth curve. In this paper we will reconstruct the above duality as a purely formal combination of a generalized form of Tate duality over p-adic fields and a form of Poincar´ e duality for curves over arbitrary fields of characteristic zero. This gives a more conceptual proof of Lichtenbaum's result and an analogue in higher dimensions

Level and Witt groups of real enriques surfaces

The Witt group of a real Enriques surface having real points is computed purely in terms of the topology of the real part. For a real Enriques surface without real points the level of the function field is shown to be 2, and the Witt group is computed in this case as well

On Albanese torsors and the elementary obstruction

We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given

Depth differential colonization and biodiversity of mycorrhizal fungi in four prairie grass species

Non-Peer ReviewedThe biodiversity of AMF at different soil depths was studied in pure stands of the grasses crested wheatgrass (Agropyron cristatum (L.) Gaertn.), switchgrass (Panicum virgatum L.), green needlegrass (Nassella viridula Trin.) and western wheatgrass (Pascopyrum smithii (Rydb.) A. Löve), growing in southwest Saskatchewan. The biodiversity of AMF was described in roots from 3 to 15, and 30 to 45 cm depth sampled in 2006 using phylogenetic and molecular tools. Soil depth reduced root colonization and influenced AMF community composition, which was dominated by six AMF phylotypes of the genus Glomus. Three AMF phylotypes were common colonizers and three were preferentially associated with some grasses. AMF communities at different depths differed from each other in all plant stands, and diversity and richness of AMF phylotypes was higher at shallow depth, except in N. viridula which showed higher richness of AMF in deeper root samples. We conclude that although some AMF are general colonizers, some AMF have a strong host preference. Our results also indicate that soil depth is a important driver of AMF phylotype distribution, and suggest the existence of niche specialization in AMF along the soil profile, which is influenced by the host plant

Quantum Langevin theory of excess noise

In an earlier work [P. J. Bardroff and S. Stenholm], we have derived a fully quantum mechanical description of excess noise in strongly damped lasers. This theory is used here to derive the corresponding quantum Langevin equations. Taking the semi-classical limit of these we are able to regain the starting point of Siegman's treatment of excess noise [Phys. Rev. A 39, 1253 (1989)]. Our results essentially constitute a quantum derivation of his theory and allow some generalizations.Comment: 9 pages, 0 figures, revte

Euler characteristics of the real points of certain varieties of algebraic tori

International audience(Conseil d'Etat, 20 oct. 2006, Commune d'Andeville - Requête n° 289234, 1re espèce - Cour administrative d'appel de Paris, 23 juin 2006, SARL Serbois - Requête n° 02PA03759, 2e espèce