arXiv
(422,153 recursos)
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Mostrando recursos 61 - 80 de 66,283
61.
Reduction of abstract homomorphisms of lattices mod p and rigidity - Khare, Chandrashekhar; Prasad, Dipendra
In this paper we pose and answer the following question in a few different
contexts: Given a homomorphism f:L_1 --> L_2 of a ``lattices'' that ``reduces
mod p'' for almost all primes p, is f ``algebraic''? For instance the lattices
may be the Mordell-Weil lattices of rational points of abelian varieties over
Q, or arithmetic groups etc. Implicit in an affirmative answer to the question
for Mordell-Weil lattices is a novel criterion for abelian varities to be
isogenous.
62.
Families of noncongruent numbers - Lemmermeyer, Franz
Let E_k denote the elliptic curve defined by y^2 = x(x^2 - k^2). We consider
the curves with k = pl, p = l = 1 mod 8 primes, and show that the density of
rank-0 curves among them is at least 1/2 by explicitly constructing nontrivial
elements in the 2-part of the Tate-Shafarevich group of E_k.
63.
On an Archimedean analogue of Tate's conjecture - Prasad, Dipendra; Rajan, C. S.
We consider an Archimedean analogue of Tate's conjecture, and verify the
conjecture in the examples of isospectral Riemann surfaces constructed by
Vigneras and Sunada. We also enunciate a simple lemma in group theory which
lies at the heart of T. Sunada's theorem about isospectral manifolds.
64.
Local points on P-adically uniformized Shimura varieties - Jordan, Bruce W.; Livné, Ron; Varshavsky, Yakov
Using the p-adic uniformization of Shimura varieties we determine, for some
of them, over which local fields they have rational points. Using this we show
in some new curve cases that the jacobians are even in the sense of Poonen and
Stoll.
65.
Galois action on class groups - Lemmermeyer, Franz
It is well known that the Galois group of an extension puts constraints on
the structure of the relative ideal class groups. Using only basic parts of the
theory of group representations, we give a unified approach to such results.
66.
Weil-etale motivic cohomology - Geisser, Thomas H.
We study Weil-etale cohomology, introduced by Lichtenbaum for varieties over
finite fields. In the first half of the paper we give an explicit description
of the base change from Weil-etale cohomology to etale cohomology. As a
consequence, we get a long exact sequence relating Weil-etale cohomology to
etale cohomology, show that for finite coefficients the cohomology theories
agree, and with rational coefficients a Weil-etale cohomology group is the
direct sum of two etale cohomology groups.
In the second half of the paper we restrict ourselves to Weil-etale
cohomology of the motivic complex. We show that for smooth projective varieties
over finite fields, finite generation of Weil-etale cohomology is...
67.
The development of the princial genus theorem - Lemmermeyer, Franz
In this article we sketch the development of the principal genus theorem from
its conception by Gauss in the case of binary quadratic forms to the
cohomological formulation of the principal genus theorem of class field theory
by Emmy Noether.
68.
Imaginary quadratic fields with Cl_2(k) = (2,2,2) - Benjamin, Elliot; Lemmermeyer, Franz; Snyder, Chip
In this article we classify the complex quadratic number fields k with
2-class group of type (2,2,2) whose Hilbert 2-class fields have a 2-class group
of rank 2, and then determine the length of their 2-class field towers.
69.
Recovering l-adic representations - Rajan, C. S.
We consider the problem of recovering l-adic representations from a knowledge
of the character values at the Frobenius elements associated to l-adic
representations constructed algebraically out of the original representations.
These results generalize earlier results in of the author concerning
refinements of strong multiplicity one for $l$-adic represntations, and a
result of Ramakrishnan recovering modular forms from a knowledge of the squares
of the Hecke eigenvalues. For example, we show that if the characters of some
tensor or symmetric powers of two absolutely irreducible l-adic representation
with the algebraic envelope of the image being connected, agree at the
Frobenius elements corresponding to a set of places of positive upper...
70.
Semistable abelian varieties with small division fields - Brumer, Armand; Kramer, Kenneth
Let $A$ be a semistable abelian variety defined over ${\bf Q}$ with bad
reduction only at one prime $p$. Let $L= {\bf Q}(A[\ell])$ be the
$\ell$-division field of $A$ for a prime $\ell$ not equal to $p$ and let
$F={\bf Q}(\mu_\ell)$ be the cyclotomic field generated by the group of
$\ell^{th}$-roots of unity. We study the varieties $A$ for which $H={\rm
Gal(L/F)}$ is "small" in the sense that $H$ is an $\ell$-group or, more
generally, that $H$ is nilpotent.
We show that if $\ell=2$ or 3 and $H$ is nilpotent then the reduction of $A$
at $p$ is totally toroidal, so its conductor is $p^{\dim A}$. The...
71.
Local-global problem for Drinfeld modules - van der Heiden, Gert-Jan
Let K be a function field and let (f) be a principal prime ideal of the ring
A, which is a subring of K. Let phi: A --> K {tau} be a Drinfeld module. In
this paper we consider the problem whether a point P in K which is a
phi(f)-fold locally at each place v of K, i.e., for each v there is a Q in K_v
such that phi(f).P = Q, is also a phi(f)-fold globally.
We also discuss the same problem in the context of elliptic curves, where it
is much simpler.
72.
Edited 4-Theta embeddings of Jacobians - Anderson, Greg W.
By the Lefschetz embedding theorem, a principally polarized $g$-dimensional
abelian variety is embedded into projective space by the linear system of $4^g$
half-characteristic theta functions. Suppose we {\em edit} this linear system
by dropping all the theta functions vanishing at the origin to order greater
than parity requires. We prove that for Jacobians the edited $4\Theta$ linear
system still defines an embedding into projective space. Moreover, we prove
that the projective models of Jacobians arising from the elementary
construction of Jacobians recently given by the author are (after passage to
linear hulls) copies of the edited $4\Theta$ model. Thus, for all compact
Riemann surfaces, we tie together algebraic and...
73.
A classical approach on cyclotomic fields and Fermat-Wiles theorem - Queme, Roland
This paper is submitted to Algebraic-Number-Theory Archives for validation by
Number Theorists Community. It is an update of the previous versions ANT-0155,
ANT-0170, ANT-0205, ANT-0237, ANT-0321, ANT-0333, and ANT-0356, of which the
first four were titled `A generalization of Eichler criterium for Fermat's Last
Theorem' and the last three were titled `A classical approach on Fermat-Wiles
theorem'.
This version contains a complete reorganization of the paper with a first
part dealing with cyclotomic fields (independently of FLT) from page 10 to 72
and a second part dealing with FLT from page 73 to end.
This version improves our previous results on cyclotomic fields and contains
several significant error...
74.
Cyclotomic Swan subgroups and primitive roots - Kohl, Timothy; Replogle, Daniel
Let $K_{m}=\Bbb{Q}(\zeta_{m})$ where $\zeta_{m}$ is a primitive $m$th root of
unity. Let $p>2$ be prime and let $C_{p}$ denote the group of order $p.$ The
ring of algebraic integers of $K_{m}$ is $\Cal{O}_{m}=\Bbb{Z}[\zeta_{m}].$ Let
$\Lambda_{m,p}$ denote the order $\Cal{O}_{m}[C_{p}]$ in the algebra
$K_{m}[C_{p}].$ Consider the kernel group $D(\Lambda_{m,p})$ and the Swan
subgroup $T(\Lambda_{m,p}).$ If $(p,m)=1$ these two subgroups of the class
group coincide. Restricting to when there is a rational prime $p$ that is prime
in $\Cal{O}_{m}$ requires $m=4$ or $q^{n}$ where $q>2$ is prime. For each such
$m$, $3 \leq m \leq 100,$ we give such a prime, and show that one may compute
$T(\Lambda_{m,p})$ as a quotient...
75.
Groupes de Selmer et accouplements - Perrin-Riou, Bernadette
Nekov\'a\v{r} vient de d\'emontrer que le rang de $E(\Q)$ pour une courbe
elliptique $E$d\'efinie sur $\Q$ est de m\^eme parit\'e que la multiplicit\'e
du z\'ero en $s=1$ de la fonction $L_{E}$ complexe associe\'e \`a $E/\Q$,
lorsque le groupe de Tate-Shafarevich est fini. La clef de la d\'emonstration
est le construction d'une forme altern\'ee et non d\'eg\'en\'er\'ee sur le
quotient de $S(K)$ par sa partie divisible. Pour construire le forme
altern\'ee, Nekov\'a\v{r} reprend compl\`etement la th\'eorie des groupes de
Selmer en utilisant la formalisme des complexes. Il obtient ainsi d'autres
applicationsen th\'eorie de Hida et autres. Nous allons faire ici cette
construction en allant au plus court et de replacer...
76.
Discrete mathematics: methods and challenges - Alon, Noga
Combinatorics is a fundamental mathematical discipline as well as an
essential component of many mathematical areas, and its study has experienced
an impressive growth in recent years. One of the main reasons for this growth
is the tight connection between Discrete Mathematics and Theoretical Computer
Science, and the rapid development of the latter. While in the past many of the
basic combinatorial results were obtained mainly by ingenuity and detailed
reasoning, the modern theory has grown out of this early stage, and often
relies on deep, well developed tools. This is a survey of two of the main
general techniques that played a crucial role in the development...
77.
Differential complexes and numerical stability - Arnold, Douglas N.
Differential complexes such as the de Rham complex have recently come to play
an important role in the design and analysis of numerical methods for partial
differential equations. The design of stable discretizations of systems of
partial differential equations often hinges on capturing subtle aspects of the
structure of the system in the discretization. In many cases the differential
geometric structure captured by a differential complex has proven to be a key
element, and a discrete differential complex which is appropriately related to
the original complex is essential. This new geometric viewpoint has provided a
unifying understanding of a variety of innovative numerical methods developed
over recent decades and...
78.
Hyperbolic systems of conservation laws in one space dimension - Bressan, Alberto
Aim of this paper is to review some basic ideas and recent developments in
the theory of strictly hyperbolic systems of conservation laws in one space
dimension. The main focus will be on the uniqueness and stability of entropy
weak solutions and on the convergence of vanishing viscosity approximations.
79.
Non linear elliptic theory and the Monge-Ampere equation - Caffarelli, Luis A.
The Monge-Ampere equation, plays a central role in the theory of fully non
linear equations. In fact we will like to show how the Monge-Ampere equation,
links in some way the ideas comming from the calculus of variations and those
of the theory of fully non linear equations.
80.
Non-linear partial differential equations in conformal geometry - Chang, Sun-Yung Alice; Yang, Paul C.
In the study of conformal geometry, the method of elliptic partial
differential equations is playing an increasingly significant role. Since the
solution of the Yamabe problem, a family of conformally covariant operators
(for definition, see section 2) generalizing the conformal Laplacian, and their
associated conformal invariants have been introduced. The conformally covariant
powers of the Laplacian form a family $P_{2k}$ with $k \in \mathbb N$ and $k
\leq \frac{n}{2}$ if the dimension $n$ is even. Each $P_{2k}$ has leading order
term $(- \Delta)^k$ and is equal to $ (- \Delta) ^k$ if the metric is flat.
61.
