arXiv
(422,153 recursos)
This is one of the most extensive subject based repositories in the world in the field of physics, mathematics, astronomy, computer sciences and quantitative biology. This is the principal site with almost 20 mirror versions around the globe. The site is supported by an extensive collection of information and background documentation. An RSS feed is available for anyone interested in keeping up-to-date with newly added materials.
Mostrando recursos 41 - 60 de 66,283
41.
The geometry of finite topology Bryant surfaces - Collin, Pascal; Hauswirth, Laurent; Rosenberg, Harold
In this paper we shall establish that properly embedded constant mean
curvature one surfaces in H^3 of finite topology are of finite total curvature
and each end is regular. In particular, this implies the horosphere is the only
simply connected such example, and the catenoid cousins the only annular
examples of this nature. In general each annular end of such a surface is
asymptotic to an end of a horosphere or an end of a catenoid cousin.
42.
A sharp bilinear cone restriction estimate - Wolff, Thomas
The purpose of this paper is to prove an essentially sharp L^2 Fourier
restriction estimate for light cones, of the type which is called bilinear in
the recent literature.
43.
Decomposable form inequalities - Thunder, Jeffrey Lin
We consider Diophantine inequalities of the kind |f(x)| \le m, where F(X) \in
Z[X] is a homogeneous polynomial which can be expressed as a product of d
homogeneous linear forms in n variables with complex coefficients and m\ge 1.
We say such a form is of finite type if the total volume of all real solutions
to this inequality is finite and if, for every n'-dimensional subspace
S\subseteq R^n defined over Q, the corresponding n'-dimensional volume for F
restricted to S is also finite. We show that the number of integral solutions x
\in Z^n to our inequality above is finite for all m if and only...
44.
On the structure theory of the Iwasawa algebra of a p-adic Lie group - Venjakob, Otmar
This paper is lead by the question whether there is a nice structure theory
of finitely generated modules over the Iwasawa algebra, i.e. the completed
group algebra, R of a p-adic analytic group G. For G without any p-torsion
element we prove that R is an Auslander regular ring. This result enables us to
give a good definition for pseudo-null R-modules. Then the category of
R-modules up to pseudo-isomorphisms is studied and we obtain a weak structure
theorem for the p-primary part of a finitely generated R-module. A local
duality theorem as well as the Auslander-Buchsbaum equality are further main
issues. The arithmetic applications to the Iwasawa theory...
45.
On the Iwasawa theory of p-adic Lie extensions - Venjakob, Otmar
In this paper the new techniques and results concerning the structure theory
of modules over non-commutative Iwasawa algebras are applied to arithmetic: we
study Iwasawa modules over p-adic Lie extensions K of number fields k "up to
pseudo-isomorphism". In particular, a close relationship is revealed between
the Selmer group of abelian varieties, the Galois group of the maximal abelian
unramified p-extension of K as well as the Galois group of the maximal abelian
outside S unramified p-extension where S is a finite set of certain places of
k. Moreover, we determine the Galois module structure of local units and other
modules arising from Galois cohomology.
46.
Designing communication networks via Hilbert modular forms - Livné, Ron
We give an explicit version of the Ramanujan-Petersson Conjecture for Hilbert
Modular Forms, and deduce the "Ramanujan" property for certain cubical
complexes. We reinterpret the results in terms of Communication Networks.
The work will appear in the proceedings of a NATO conference on "Applications
of Algebraic Geometry to Coding Theory, Physics, and Computation", which took
place in Eilat, Israel, February 25 - March 1s 2001, to be published by Kluwer.
47.
Octahedral Galois representations arising from Q-curves of degree 2 - Fernández-González, Julio; Lario, Joan-Carles; Rio, Anna
Generically, one can attach to a Q-curve C octahedral representations
Gal(Qbar/Q) --> GL(2,Fbar_3) coming from the Galois action on the 3-torsion of
those abelian varieties of GL_2-type whose building block is C. When C is
defined over a quadratic field and has an isogeny of degree 2 to its Galois
conjugate, there exist such representations having image into GL(2,F_9). Going
the other way, we can ask which mod 3 octahedral representations of Gal(Qbar/Q)
arise from Q-curves in the above sense. We characterize those arising from
quadratic Q-curves of degree 2. The approach makes use of Galois embedding
techniques in GL(2,F_9), and the characterization can be given in terms...
48.
Legendre elliptic curves over finite fields - Auer, Roland; Top, Jaap
We show that every elliptic curve over a finite field of odd characteristic
whose number of rational points is divisible by 4 is isogenous to an elliptic
curve in Legendre form, with the sole exception of a minimal respectively
maximal elliptic curve. We also collect some results concerning the
supersingular Legendre parameters.
49.
Arithm\'etique des courbes elliptiques a r\'eduction supersinguliere en p - Perrin-Riou, Bernadette
We review the main conjecture for an elliptic curve on $\Q$ having good
supersingular reduction at $p$ and give some consequences of it. Then we define
the notion of $\lambda$-invariant and of $\mu$- invariant in this situation,
generalizing a work of Kurihara and deduce from it the behaviour of the order
of the group of Shafarevich-Tate along the cyclotomique $\Z_p$-extension. By
examples, we give some arguments which, by allying theorems and numeral
calculations, allow to calculate the order of the $p$-primary part of the group
of Shafarevich-Tate in not yet known cases (non trivial Shafarevich-Tate group,
curves of rank greater than $ 1$).
50.
Greenberg's conjecture and cyclotomic towers - Marshall, David C.
We describe Greenberg's pseudo-null conjecture, and prove a result describing
conditions under which the pseudo-null conjecture for a number field $K$
implies the conjecture for finite extensions of $K$. We then apply the result
to the cyclotomic $\mathbb{Z}_p$-tower above a cyclotomic field of prime roots
of unity, verifying the conjecture for a large class of cyclotomic fields.
51.
The Oka principle for sections of subelliptic submersions - Forstneric, Franc
Let X and Y be complex manifolds. One says that maps from X to Y satisfy the
Oka principle if the inclusion of the space of holomorphic maps from X to Y
into the space of continuous maps is a weak homotopy equivalence. In 1957 H.
Grauert proved the Oka principle for maps from Stein manifolds to complex Lie
groups and homogeneous spaces, as well as for sections of fiber bundles with
homogeneous fibers over a Stein base. In 1989 M. Gromov extended Grauert's
result to sections of submersions over a Stein base which admit dominating
sprays over small open sets in the base; for proof see...
52.
On Cebotarev sets - Wingberg, Kay
In this paper we define a topology with sufficiently good properties on the
set of prime ideals of a number field.
53.
Modules over Iwasawa algebras - Coates, John H.; Schneider, Peter; Sujatha, Ramdoria
Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall
that the Iwasawa algebra $\Lambda(G)$ is defined to be the completed group ring
of $G$ over the ring of $p$-adic integers. Interesting examples of finitely
generated modules over $\Lambda(G),$ in which $G$ is the image of Galois in the
automorphism group of a $p$-adic Galois representation, abound in arithmetic
geometry. The study of such $\Lambda(G)$-modules arising from arithmetic
geometry can be thought of as a natural generalization of Iwasawa theory. One
of the cornerstones of classical Iwasawa theory is the fact that, when $G$ is
the additive group of $p$-adic integers, a good...
54.
Counting nilpotent Galois extensions - Klueners, Juergen; Malle, Gunter
We obtain strong information on the asymptotic behaviour of the counting
function for nilpotent Galois extensions with bounded discriminant of arbitrary
number fields. This extends previous investigations for the case of abelian
groups. In particular, the result confirms a conjecture by the second author on
this function for arbitrary groups in the nilpotent case. We further prove
compatibility of the conjecture with taking wreath products with the cyclic
group of order 2 and give examples in degree up to 8.
55.
Extensions of number fields with wild ramification of bounded depth - Hajir, Farshid; Maire, Christian
We consider p-extensions of number fields such that the filtration of the
Galois group by higher ramification groups is of prescribed finite length. We
extend well-known properties of tame extensions to this more general setting;
for instance, we show that these towers, when infinite, are ``asymptotically
good'' (an explicit bound for the root discriminant is given). We study the
difficult problem of bounding the relation-rank of the Galois groups in
question. Results of Gordeev and Wingberg imply that the relation-rank can tend
to infinity when the set of ramified primes is fixed but the length of the
ramification filtration becomes large. We show that all p-adic representations
of these...
56.
Stein Domains in Complex Surfaces - Forstneric, Franc
Let S be a closed connected real surface and f a smooth embedding or
immersion of S into a complex surface X. Assuming that the number of complex
points of the immersion (counted with algebraic multiplicities) is non-positive
we prove that f can be uniformly approximated by an isotopic immersion g whose
image g(S) in X has a basis of open Stein neighborhoods which are homotopy
equivalent to g(S). We obtain precise results for surfaces in the complex
projective plane CP^2 and find an immersed symplectic sphere in CP^2 with a
Stein neighborhood. Conversely, the generalized adjunction inequality for
embedded oriented real surfaces in complex surfaces shows that...
57.
On trisecant lines to White surfaces - Bertin, Marie-Amelie
In this work we show that the only White surface in the projective 5-space
having an excess of trisecant lines is the polygonal surface constructed by C.
Segre. The proof follows the line of B.Gambier's beautiful approach to this
question and is intended to give it modern rigour. This has some implications
on the geometry of the generic point of the principal componant of the Hilbert
scheme of 18 points in the projective plane special in degree 5.
58.
Some genus 3 curves with many points - Auer, Roland; Top, Jaap
Using an explicit family of plane quartic curves, we prove the existence of a
genus 3 curve over any finite field of characteristic 3 whose number of
rational points stays within a fixed distance from the Hasse-Weil-Serre upper
bound. We also provide an intrinsic characterization of so-called Legendre
elliptic curves.
59.
Explicit descent over X(3) and X(5) - O'Neil, Catherine H.
We split the program of explicit descent of elliptic curves into two parts.
For $n=3$ and $n=5,$ we first display a model for the universal elliptic curve
$E$ with full level $n$ structure and describe the map of rational points of
$E$ to the cohomology group $H^1(G, E[n]).$ Second, we find models in
$\PP^{n-1}$ of principal homogeneous spaces of $E$ corresponding to all
possible elements of $H^1(G, E[n]),$ i.e. for those elements with trivial
period-index obstruction. For this we use the relationship established in
\cite{me2} between the period-index obstruction and the norm symbol, a
generalization of the Hilbert symbol.
60.
Nontrivial Galois module structure of cyclotomic fields - Conrad, Marc; Replogle, Daniel R.
We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial
Galois module structure if the rings of integers have the property that
$\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-module. The work of Greither,
Replogle, Rubin, and Srivastav shows that for each algebraic number field other
than the rational numbers there will exist infinitely many primes $l$ so that
for each there is a tame Galois field extension of degree $l$ so that $L/K$ has
nontrivial Galois module structure. However, the proof does not directly yield
specific primes $l$ for a given algebraic number field $K.$ For $K$ any
cyclotomic field we find an explicit $l$ so...
41.
