3,300 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

### X-ray sources and their optical counterparts in the globular cluster M 22

Using XMM-Newton EPIC imaging data, we have detected 50 low-luminosity X-ray
sources in the field of view of M 22, where 5 +/- 3 of these sources are likely
to be related to the cluster. Using differential optical photometry, we have
identified probable counterparts to those sources belonging to the cluster.
Using X-ray spectroscopic and timing studies, supported by the optical colours,
we propose that the most central X-ray sources in the cluster are cataclysmic
variables, millisecond pulsars, active binaries and a blue straggler. We also
identify a cluster of galaxies behind this globular cluster.Comment: 11 pages, 7 figures, accepted for publication in A&

### Representations and $K$-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension
with certain finiteness conditions of the type satisfied by arithmetic groups.
We define a representation ring for $\Gamma$, determined on its elements of
finite order, which is of finite type. Then we determine the contribution of
this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact
formula for the difference in terms of the cohomology of the centralizers of
elements of finite order in $\Gamma$.Comment: 4 page

### High resolution imaging with Fresnel interferometric arrays: suitability for exoplanet detection

We propose a new kind of interferometric array that yields images of high
dynamic range and large field. The numerous individual apertures in this array
form a pattern related to a Fresnel zone plate. This array can be used for
astrophysical imaging over a broad spectral bandwidth spanning from the U.V.
(50 nanometers) to the I.R. (20 microns). Due to the long focal lengths
involved, this instrument requires formation-flying of two space borne vessels.
We present the concept and study the S/N ratio in different situations, then
apply these results to probe the suitability of this concept to detect
exoplanets.Comment: 12 pages, 19 figures, to be published in A&

### New reductions of integrable matrix PDEs: $Sp(m)$-invariant systems

We propose a new type of reduction for integrable systems of coupled matrix
PDEs; this reduction equates one matrix variable with the transposition of
another multiplied by an antisymmetric constant matrix. Via this reduction, we
obtain a new integrable system of coupled derivative mKdV equations and a new
integrable variant of the massive Thirring model, in addition to the already
known systems. We also discuss integrable semi-discretizations of the obtained
systems and present new soliton solutions to both continuous and semi-discrete
systems. As a by-product, a new integrable semi-discretization of the Manakov
model (self-focusing vector NLS equation) is obtained.Comment: 33 pages; (v4) to appear in JMP; This paper states clearly that the
elementary function solutions of (a vector/matrix generalization of) the
derivative NLS equation can be expressed as the partial $x$-derivatives of
elementary functions. Explicit soliton solutions are given in the author's
talks at http://poisson.ms.u-tokyo.ac.jp/~tsuchida

### On a differential inclusion related to the Born-Infeld equations

We study a partial differential relation that arises in the context of the
Born-Infeld equations (an extension of the Maxwell's equations) by using
Gromov's method of convex integration in the setting of divergence free fields

### 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

### Invariance Properties of Inviscid Fluids of Grade n

Revisited and completed version, 18 pages and 2 figures.International audienceFluids of grade n are continuous media in dynamic changes of phases avoiding the surfaces of discontinuity and representing the capillary layers in liquid-vapour interfaces. We recall the thermodynamic form of the equation of motion for inviscid fluids of grade n. First integrals and theorems of circulation are deduced. A general classification of flows is proposed

### Alternating groups and moduli space lifting Invariants

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of
degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves
Fried-Serre on deciding when sphere covers with odd-order branching lift to
unramified Spin covers. We produce Hurwitz-Torelli automorphic functions on
Hurwitz spaces, and draw Inverse Galois conclusions. Example: Absolute spaces
of 3-cycle covers with +1 (resp. -1) lift invariant carry canonical even (resp.
odd) theta functions when r is even (resp. odd). For inner spaces the result is
independent of r. Another use appears in,
http://www.math.uci.edu/~mfried/paplist-mt/twoorbit.html, "Connectedness of
families of sphere covers of A_n-Type." This shows the M(odular) T(ower)s for
the prime p=2 lying over Hurwitz spaces first studied by,
http://www.math.uci.edu/~mfried/othlist-cov/hurwitzLiu-Oss.pdf, Liu and
Osserman have 2-cusps. That is sufficient to establish the Main Conjecture: (*)
High tower levels are general-type varieties and have no rational points.For
infinitely many of those MTs, the tree of cusps contains a subtree -- a spire
-- isomorphic to the tree of cusps on a modular curve tower. This makes
plausible a version of Serre's O(pen) I(mage) T(heorem) on such MTs.
Establishing these modular curve-like properties opens, to MTs, modular
curve-like thinking where modular curves have never gone before. A fuller html
description of this paper is at
http://www.math.uci.edu/~mfried/paplist-cov/hf-can0611591.html .Comment: To appear in the Israel Journal as of 1/5/09; v4 is corrected from
proof sheets, but does include some proof simplification in \S

- âŠ