809 research outputs found
A categorical proof of the Parshin reciprocity laws on algebraic surfaces
We define and study the 2-category of torsors over a Picard groupoid, a
central extension of a group by a Picard groupoid, and commutator maps in this
central extension. Using it in the context of two-dimensional local fields and
two-dimensional adelic theory we obtain the two-dimensional tame symbol and a
new proof of Parshin reciprocity laws on an algebraic surface.Comment: 41 pages; final version, to appear in Algebra & Number Theor
On a Ring of Formal Pseudo-differential Operators
We study the notion of non-commumative higher dimensional local fields. A
simplest example is the ring P of formal pseudo- differential operators. As an
application we extend the KP hierarchy to the space .Comment: LaTe
Two-dimensional Id\`eles with Cycle Module Coefficients
We give a theory of id\`eles with coefficients for smooth surfaces over a
field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but
handling cycle module sheaves instead of quasi-coherent ones. We prove that
they give a flasque resolution of the cycle module sheaves in the Zariski
topology. As a technical ingredient we show the Gersten property for cycle
modules on equicharacteristic complete regular local rings, which might be of
independent interest.Comment: major change in exposition, streamlined, removed incorrect claim
about product map (many thanks to S. Gorchinskiy for pointing this out to
me), bibliography update
Effect of a Magnetic Field on the Dipole Echo in Glasses with Nuclear Quadrupole Moments
The effect of a magnetic field on the dipole echo amplitude in glasses at
temperatures of about 10 mK caused by nonspherical nuclei with electric
quadrupole moments has been studied theoretically. It has been shown that in
this case, the two-level systems (TLS's) that determine the glass properties at
low temperatures are transformed into more complicated multilevel systems.
These systems have new properties as compared to usual TLS's and, in
particular, exhibit oscillations of electric dipole echo amplitude in magnetic
field. A general formula that describes the echo amplitude in an arbitrary
split TLS has been derived with perturbation theory. Detailed analytic and
numerical analysis of the formula has been performed. The theory agrees
qualitatively and quantitatively well with experimental data.Comment: 5 pages, 3 figure
Harmonic analysis on local fields and adelic spaces I
We develop a harmonic analysis on objects of some category of
infinite-dimensional filtered vector spaces over a finite field. It includes
two-dimensional local fields and adelic spaces of algebraic surfaces defined
over a finite field. The main result is the theory of the Fourier transform on
these objects and two-dimensional Poisson formulas.Comment: 69 pages; corrected typos and inserted some changes into the last
sectio
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