3,207 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
Splittings of groups and intersection numbers
We prove algebraic analogues of the facts that a curve on a surface with
self-intersection number zero is homotopic to a cover of a simple curve, and
that two simple curves on a surface with intersection number zero can be
isotoped to be disjoint.Comment: 40 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper6.abs.htm
Representations and -theory of Discrete Groups
Let 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 , determined on its elements of
finite order, which is of finite type. Then we determine the contribution of
this ring to the topological -theory , obtaining an exact
formula for the difference in terms of the cohomology of the centralizers of
elements of finite order in .Comment: 4 page
One Relator Quotients of Graph Products
In this paper, we generalise Magnus' Freiheitssatz and solution to the word
problem for one-relator groups by considering one relator quotients of certain
classes of right-angled Artin groups and graph products of locally indicable
polycyclic groups
Extended diffeomorphism algebras in (quantum) gravitational physics
We construct an explicit representation of the algebra of local
diffeomorphisms of a manifold with realistic dimensions. This is achieved in
the setting of a general approach to the (quantum) dynamics of a physical
system which is characterized by the fundamental role assigned to a basic
underlying symmetry. The developed mathematical formalism makes contact with
the relevant gravitational notions by means of the addition of some extra
structure. The specific manners in which this is accomplished, together with
their corresponding physical interpretation, lead to different gravitational
models. Distinct strategies are in fact briefly outlined, showing the
versatility of the present conceptual framework.Comment: 20 pages, LATEX, no figure
Point counting on reductions of CM elliptic curves
We give explicit formulas for the number of points on reductions of elliptic
curves with complex multiplication by any imaginary quadratic field. We also
find models for CM -curves in certain cases. This generalizes
earlier results of Gross, Stark, and others.Comment: Minor corrections. To appear in Journal of Number Theor
Proalgebraic crossed modules of quasirational presentations
We introduce the concept of quasirational relation modules for discrete and
pro- presentations of discrete and pro- groups and show that aspherical
presentations and their subpresentations are quasirational. In the pro--case
quasirationality of pro--groups with a single defining relation holds. For
every quasirational (pro-)relation module we construct the so called
-adic rationalization, which is a pro-fd-module
. We provide the isomorphisms
and , where and
stands for continuous prounipotent completions and corresponding
prounipotent presentations correspondingly. We show how
embeds into a sequence of abelian prounipotent
groups. This sequence arises naturally from a certain prounipotent crossed
module, the latter bring concrete examples of proalgebraic homotopy types. The
old-standing open problem of Serre, slightly corrected by Gildenhuys, in its
modern form states that pro--groups with a single defining relation are
aspherical. Our results give a positive feedback to the question of Serre.Comment: This is a corrected version of the paper which appeared in the
Extended Abstracts Spring 2015, Interactions between Representation Theory,
Algebraic Topology and Commutative Algebra, Research Perspectives CRM
Barcelona, Vol.5, 201
- …