949 research outputs found
Harmonic analysis and the Riemann-Roch theorem
This paper is a continuation of papers: arXiv:0707.1766 [math.AG] and
arXiv:0912.1577 [math.AG]. Using the two-dimensional Poisson formulas from
these papers and two-dimensional adelic theory we obtain the Riemann-Roch
formula on a projective smooth algebraic surface over a finite field.Comment: 7 pages; to appear in Doklady Mathematic
Adelic constructions of direct images for differentials and symbols
For a projective morphism of an smooth algebraic surface onto a smooth
algebraic curve , both given over a perfect field , we construct the
direct image morphism in two cases: from to
and when from to
. (If i=2, then the last map is the Gysin map from
to .)
To do this in the first case we use the known adelic resolution for sheafs
and . In the second case we construct a -adelic
resolution of a sheaf . And thus we reduce the direct image morphism to
the construction of some residues and symbols from differentials and symbols of
2-dimensional local fields associated with pairs ( is a closed
point on an irredicuble curve ) to 1-dimensional local fields
associated with closed points on the curve .
We prove reciprocity laws for these maps.Comment: 29 pages, modified version of the article, appeared in
"Matematicheskiy Sbornik" 5(188) (1997
n-dimensional local fields and adeles on n-dimensional schemes
It is a survey paper on n-dimensional local fields and adeles on
n-dimensional schemes.Comment: 30 pages, submitted for publication in the LMS Lecture Notes Serie
The continuum gauge field-theory model for low-energy electronic states of icosahedral fullerenes
The low-energy electronic structure of icosahedral fullerenes is studied
within the field-theory model. In the field model, the pentagonal rings in the
fullerene are simulated by two kinds of gauge fields. The first one,
non-abelian field, follows from so-called K spin rotation invariance for the
spinor field while the second one describes the elastic flow due to pentagonal
apical disclinations. For fullerene molecule, these fluxes are taken into
account by introducing an effective field due to magnetic monopole placed at
the center of a sphere. Additionally, the spherical geometry of the fullerene
is incorporated via the spin connection term. The exact analytical solution of
the problem (both for the eigenfunctions and the energy spectrum) is found.Comment: 9 pages, 2 figures, submitted to European Physical Journal
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