152 research outputs found
Galois deformation theory for norm fields and flat deformation rings
Let be a finite extension of , and choose a uniformizer
, and put . We introduce a new
technique using restriction to \Gal(\ol K/K_\infty) to study flat deformation
rings. We show the existence of deformation rings for \Gal(\ol
K/K_\infty)-representations ``of height '' for any positive
integer , and we use them to give a variant of Kisin's proof of connected
component analysis of a certain flat deformation rings, which was used to prove
Kisin's modularity lifting theorem for potentially Barsotti-Tate
representations. Our proof does not use the classification of finite flat group
schemes, so it avoids Zink's theory of windows and displays when .
This \Gal(\ol K/K_\infty)-deformation theory has a good analogue in
positive characteristics analogue of crystalline representations in the sense
of Genestier-Lafforgue. In particular, we obtain a positive characteristic
analogue of crystalline deformation rings, and can analyze their local
structure
The Lyman-alpha forest and WMAP year three
A combined analysis of Cosmic Microwave Background (CMB) and Lyman-a forest
data allows to constrain the matter power spectrum from small scales of about 1
Mpc/h all the way to the horizon scale. The long lever arm and complementarity
provided by such an analysis has previously led to a significant tightening of
the constraints on the shape and the amplitude of the power spectrum of
primordial density fluctuations. We present here a combined analysis of the
WMAP three year results with Lyman-a forest data. The amplitude of the matter
power spectrum sigma_8 and the spectral index ns inferred from the joint
analysis with high resolution Lyman-a forest data and low resolution Lyman-a
forest data as analyzed by Viel & Haehnelt (2006) are consistent with the new
WMAP results to within 1 sigma. The joint analysis with the mainly low
resolution data as analysed by McDonald et al. (2005) suggests a value of
sigma_8 which is ~ 2 sigma higher than that inferred from the WMAP three year
data alone. The joint analysis of the three year WMAP and the Lyman-a forest
data also does not favour a running of the spectral index. The best fit values
for a combined analysis of the three year WMAP data, other CMB data, 2dF and
the Lyman-a forest data are (sigma_8, ns) = (0.78\pm 0.03,0.96 \pm 0.01).Comment: 5 pages, 4 figs, 2 tables. MNRAS letters in pres
Cohomologie syntomique: liens avec les cohomologies étale et rigide
26 pagesSyntomic cohomology here defined yields a link between rigid cohomology and etale cohomology, viewing the last one as the fixed points under Frobenius of the former one. Let V be a complete discrete valuation ring, with perfect residue field k = V/m of characteristic p > 0 and fraction field K of characteristic 0. Having defined syntomic cohomology with compact supports of an abelian sheaf G on a k-scheme X, we show that it coincides with etale cohomology with compact supports when G is a lisse sheaf. If moreover the convergent F-isocrystal associated to G comes from an overconvergent isocrystal E, then the rigid cohomology of E expresses as a limit of syntomic cohomologies: then the etale cohomology with compact supports of G is the fixed points of Frobenius acting on the rigid cohomology of E
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