3,156 research outputs found
Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras
We prove an analogue of the Tate conjecture on homomorphisms of abelian
varieties over infinite cyclotomic extensions of finitely generated fields of
characteristic zero.Comment: 9 page
Automorphisms and forms of simple infinite-dimensional linearly compact Lie superalgebras
We describe the group of continuous automorphisms of all simple
infinite-dimensional linearly compact Lie superalgebras and use it in order to
classify F-forms of these superalgebras over any field F of characteristic
zero.Comment: 24 page
From perinuclear factor to citrulline, a target structure for autoantibodies in rheumatoid arthritis
Finiteness properties of cubulated groups
We give a generalized and self-contained account of Haglund-Paulin's
wallspaces and Sageev's construction of the CAT(0) cube complex dual to a
wallspace. We examine criteria on a wallspace leading to finiteness properties
of its dual cube complex. Our discussion is aimed at readers wishing to apply
these methods to produce actions of groups on cube complexes and understand
their nature. We develop the wallspace ideas in a level of generality that
facilitates their application.
Our main result describes the structure of dual cube complexes arising from
relatively hyperbolic groups. Let H_1,...,H_s be relatively quasiconvex
codimension-1 subgroups of a group G that is hyperbolic relative to
P_1,...,P_r. We prove that G acts relatively cocompactly on the associated dual
CAT(0) cube complex C. This generalizes Sageev's result that C is cocompact
when G is hyperbolic. When P_1,...,P_r are abelian, we show that the dual
CAT(0) cube complex C has a G-cocompact CAT(0) truncation.Comment: 58 pages, 12 figures. Version 3: Revisions and slightly improved
results in Sections 7 and 8. Several theorem numbers have changed from the
previous versio
Homotopy nilpotent groups
We study the connection between the Goodwillie tower of the identity and the
lower central series of the loop group on connected spaces. We define the
simplicial theory of homotopy n-nilpotent groups. This notion interpolates
between infinite loop spaces and loop spaces. We prove that the set-valued
algebraic theory obtained by applying is the theory of ordinary
n-nilpotent groups and that the Goodwillie tower of a connected space is
determined by a certain homotopy left Kan extension. We prove that n-excisive
functors of the form have values in homotopy n-nilpotent groups.Comment: 16 pages, uses xy-pic, improved exposition, submitte
Experience in the exploitation of a large control system
Experience of a four-year exploitation of the large control system of the CERN PS accelerator complex is presented with special emphasis on the parameters which are very sensitive to the exploitation team productivity. The software tools suite used in this daily maintenance is described and a particular analysis of the power and benefits of advance software technology used for the architecture of this suite is explained. The integration of this suite in the Control System is presented, as well as its use in the Control System development phase. Some considerations of the potential benefit of an Object Oriented equipment access are outlined
On p-adic lattices and Grassmannians
It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive
group G over a field k, carry the geometric structure of an inductive limit of
projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for
G. From the point of view of number theory it would be interesting to obtain an
analogous geometric interpretation of quotients of the form
G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of
p-typical Witt vectors, k is a perfect field of characteristic p and G is a
reductive group scheme over W(k). The present paper is an attempt to describe
which constructions carry over from the function field case to the p-adic case,
more precisely to the situation of the p-adic affine Grassmannian for the
special linear group G=SL_n. We start with a description of the R-valued points
of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R),
where R is a perfect k-algebra. In order to obtain a link with geometry we
further construct projective k-subvarieties of the multigraded Hilbert scheme
which map equivariantly to the p-adic affine Grassmannian. The images of these
morphisms play the role of Schubert varieties in the p-adic setting. Further,
for any reduced k-algebra R these morphisms induce bijective maps between the
sets of R-valued points of the respective open orbits in the multigraded
Hilbert scheme and the corresponding Schubert cells of the p-adic affine
Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math.
Zeitschrift, of the previously published preprint "On p-adic loop groups and
Grassmannians
Integral closure of rings of integer-valued polynomials on algebras
Let be an integrally closed domain with quotient field . Let be a
torsion-free -algebra that is finitely generated as a -module. For every
in we consider its minimal polynomial , i.e. the
monic polynomial of least degree such that . The ring consists of polynomials in that send elements of back to
under evaluation. If has finite residue rings, we show that the
integral closure of is the ring of polynomials in which
map the roots in an algebraic closure of of all the , ,
into elements that are integral over . The result is obtained by identifying
with a -subalgebra of the matrix algebra for some and then
considering polynomials which map a matrix to a matrix integral over . We
also obtain information about polynomially dense subsets of these rings of
polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix,
integral closure, pullback, polynomially dense set. accepted for publication
in the volume "Commutative rings, integer-valued polynomials and polynomial
functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201
Two limit cases of Born-Infeld equations
International audienceWe study two limit cases \l \rightarrow \infty and \l \rightarrow 0 in Born-Infeld equations. Here the parameter \l >0 is interpreted as the maximal electric field in the electromagnetic theory and the case \l = 0 corresponds to the string theory. Formal limits are governed by the classical Maxwell equations and pressureless magnetohydrodynamics system, respectively. For studying the limit \l \rightarrow \infty, a new scaling is introduced. We give the relations between these limits and Brenier high and low field limits. Finally, using compensated compactness arguments, the limits are rigorously justified for global entropy solutions in in one space dimension, based on derived uniform estimates and techniques for linear Lagrangian systems
Strongly bounded groups and infinite powers of finite groups
We define a group as strongly bounded if every isometric action on a metric
space has bounded orbits. This latter property is equivalent to the so-called
uncountable strong cofinality, recently introduced by G. Bergman.
Our main result is that G^I is strongly bounded when G is a finite, perfect
group and I is any set. This strengthens a result of Koppelberg and Tits. We
also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups
with Property (FH)". To appear in Comm. Algebr
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