577,618 research outputs found
Rational points on varieties and Morita equivalences of -algebras
Let be a projective variety over a number field
and let be the Serre -algebra of . We construct a
functor , such that the -isomorphic
(-isomorphic, resp.) varieties map to the Morita equivalent
(isomorphic, resp.) -algebras . In other words, the
isomorphisms of the algebra preserve the -rational
points of , while the Morita equivalences of correspond
to the twists of the variety . We apply the result to the arithmetic
geometry of the rational elliptic curves.Comment: 7 pages; an updat
The Relative Lie Algebra Cohomology of the Weil Representation of SO(n,1)
In Part 1 of this paper we construct a spectral sequence converging to the
relative Lie algebra cohomology associated to the action of any subgroup of
the symplectic group on the polynomial Fock model of the Weil representation,
see Section 7. These relative Lie algebra cohomology groups are of interest
because they map to the cohomology of suitable arithmetic quotients of the
symmetric space of . We apply this spectral sequence to the case in Sections 8, 9, and 10 to compute the relative Lie
algebra cohomology groups . Here is Minkowski space and
is the subspace of consisting of all products of
polynomials with the Gaussian. In Part 2 of this paper we compute the
cohomology groups using spectral theory and representation theory. In Part 3 of this paper
we compute the maps between the polynomial Fock and cohomology groups
induced by the inclusions .Comment: 64 pages, 5 figure
Improving the surface brightness-color relation for early-type stars using optical interferometry
The aim of this work is to improve the SBC relation for early-type stars in
the color domain, using optical interferometry.
Observations of eight B- and A-type stars were secured with the VEGA/CHARA
instrument in the visible. The derived uniform disk angular diameters were
converted into limb darkened angular diameters and included in a larger sample
of 24 stars, already observed by interferometry, in order to derive a revised
empirical relation for O, B, A spectral type stars with a V-K color index
ranging from -1 to 0. We also took the opportunity to check the consistency of
the SBC relation up to using 100 additional measurements. We
determined the uniform disk angular diameter for the eight following stars:
Ori, Per, Cyg, Her, Aql, Peg,
Lyr, and Cyg with V-K color ranging from -0.70 to 0.02 and
typical precision of about . Using our total sample of 132 stars with
colors index ranging from about to , we provide a revised SBC
relation. For late-type stars (), the results are consistent
with previous studies. For early-type stars (), our new
VEGA/CHARA measurements combined with a careful selection of the stars
(rejecting stars with environment or stars with a strong variability), allows
us to reach an unprecedented precision of about 0.16 magnitude or
in terms of angular diameter.Comment: 13 pages, 5 figures, accepted for publication in A&
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