Subject: Re: new Hopf listings
From: Mark Hovey
Date: 04 Aug 2005 09:50:05 -0400
---------------------------
There are 11 new papers this time, from Behrens (3), Behrens-Lawson,
Chebolu, DavisDaniel, Hovey, Lueck, Morava, Neusel, and
Neusel-Wisniewski.
Mark Hovey
New papers appearing on hopf between 7/1/05 and 8/1/05
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Behrens/rootkin/rootkin
Title: Some root invariants at the prime 2
Author(s): Mark Behrens
Author's e-mail address: mbehrens@math.mit.edu
Abstract:
The first part of this paper consists of lecture notes which summarize the
machinery of filtered root invariants. A conceptual notion of "homotopy
Greek
letter element" is also introduced, and evidence is presented that it may
be
related to the root invariant. In the second part we compute some low
dimensional root invariants of v_1-periodic elements at the prime 2.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Behrens/rootpub/rootpub
Title: Root invariants in the Adams spectral sequence
Author(s): Mark Behrens
Author's e-mail address: mbehrens@math.mit.edu
Abstract:
Let E be a ring spectrum for which the E-Adams spectral sequence
converges.
We define a variant of Mahowald's root invariant called the `filtered root
invariant' which takes values in the E_1 term of the E-Adams spectral
sequence.
The main theorems of this paper concern when these filtered root
invariants
detect the actual root invariant, and explain a relationship between
filtered
root invariants and differentials and compositions in the E-Adams spectral
sequence. These theorems are compared to some known computations of root
invariants at the prime 2. We use the filtered root invariants to compute
some
low dimensional root invariants of v_1-periodic elements at the prime 3.
We
also compute the root invariants of some infinite v_1-periodic families of
elements at the prime 3.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Behrens/K2S/K2S
Title: A modular description of the K(2)-local sphere at the prime 3
Author(s): Mark Behrens
Author's e-mail address: mbehrens@math.mit.edu
Abstract:
Using degree N isogenies of elliptic curves, we produce a spectrum Q(N).
This
spectrum is built out of spectra related to tmf. At p=3 we show that the
K(2)-local sphere is built out of Q(2) and its K(2)-local
Spanier-Whitehead
dual. This gives a conceptual reinterpretation a resolution of Goerss,
Henn,
Mahowald, and Rezk.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Behrens-Lawson/dense
Title: Isogenies of elliptic curves and the Morava stabilizer group
Authors: Mark Behrens and Tyler Lawson
Author's e-mail address: mbehrens@math.mit.edu, tlawson@math.mit.edu
Abstract:
Let MS_2 be the p-primary second Morava stabilizer group, C a
supersingular elliptic curve over \br{FF}_p, O the ring of endomorphisms
of C, and \ell a topological generator of Z_p^x (respectively
Z_2^x/{+-1} if p = 2). We show that for p > 2 the group \Gamma
\subseteq O[1/\ell]^x of quasi-endomorphisms of degree a power of \ell
is dense in MS_2. For p = 2, we show that \Gamma is dense in an index 2
subgroup of MS_2.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu/KS
Title: Krull-Schmidt decompositions for thick subcategories
Author: Sunil Chebolu
Email address: schebolu@uwo.ca
AMS classifictaion numbers: Primary: 55p42; Secondary: 18E30
Address: Department of Mathematics, University of Western Ontario,
London, ON, N6A 5B7
Abstract: Following Krause, we prove Krull-Schmidt theorems for thick
subcategories of various triangulated categories: derived categories of
rings, noetherian stable homotopy categories, stable module categories
over Hopf algebras, and the stable homotopy category of spectra. In all
these categories, it is shown that the thick ideals of small objects
decompose uniquely into indecomposable thick ideals. Some consequences
of these decomposition results are also discussed. In particular, it is
shown that all these decompositions respect $K$-theory
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/p1v5ams
Title: Homotopy fixed points for L_K(n)(E_n ^ X) using the continuous
action
(Revised version)
Author: Daniel Davis
E-mail: dgdavis@math.purdue.edu
Address: Purdue University, Department of Mathematics, 150 N. University
Street, West Lafayette, IN 47907-2067
Abstract: Let G be a closed subgroup of G_n, the extended Morava
stabilizer
group. Let E_n be the Lubin-Tate spectrum, let X be an arbitrary spectrum
with trivial G-action, and define E^(X) to be L_K(n)(E_n ^ X). We prove
that E^(X) is a continuous G-spectrum with a G-homotopy fixed point
spectrum,
defined with respect to the continuous action. Also, we construct a
descent
spectral sequence whose abutment is the homotopy groups of the G-homotopy
fixed point spectrum of E^(X). We show that the homotopy fixed points of
E^(X) come from the K(n)-localization of the homotopy fixed points of the
spectrum (F_n ^ X).
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/Hovey/freyd
On Freyd's generating hypothesis
Mark Hovey
mhovey@wesleyan.edu
We revisit Freyd's generating hypothesis in stable homotopy theory. We
derive new equivalent forms of the generating hypothesis and some new
consequences of it. A surprising one is that $I$, the Brown-Comenetz
dual of the sphere and the source of many counterexamples in stable
homotopy, is the cofiber of a self map of a wedge of spheres. We also
show that a consequence of the generating hypothesis, that the homotopy
of a finite spectrum that is not a wedge of spheres can never be
finitely generated as a module over $\pi_{*}S$, is in fact true for
finite torsion spectra.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Lueck/lueck_tkcsr
Title: Rational Computations of the Topological K-Theory of Classifying
Spaces of Discrete Groups
Author: Wolfgang Lueck
AMS Classification Numbers: 55N15
Address: Wolfgang Lueck
Mathematisches Institut der Westfaelischen Wilhelms-Universitaet
Einsteinstr. 62
48149 Muenster
Germany
Email: lueck@math.uni-muenster.de
xxx-archive: KT/0507237
Abstract: We compute rationally the topological (complex) K-theory of
the classifying space BG of a discrete group provided that G has a
cocompact G-CW-model for its classifying space for proper G-actions. For
instance word-hyperbolic groups and cocompact discrete subgroups of
connected Lie groups satisfy this assumption. The answer is given in
terms of the group cohomology of G and of the centralizers of finite
cyclic subgroups of prime power order. We also analyze the
multiplicative structure.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/Morava/Rosendal
Title: Toward a fundamental groupoid for tensor triangulated categories
Author: Jack Morava, jack@math.jhu.edu
AMS classification: 11G, 19F, 57R, 81T
Abstract: Notes for a talk at the conference on arithmetic of structured
ring spectra; Rosendal, Norway, August 19 - 28 2005:
This very speculative talk suggests that a theory of fundamental groupoids
for tensor triangulated categories could be used to describe the ring of
integers as the singular fiber in a family of ring-spectra parametrized by
a structure space for the stable homotopy category, and that Bousfield
localization might be part of a theory of `nearby' cycles for stacks or
orbifolds.
10.
http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel/survey
Degree bounds--an invitation to postmodern invariant theory
Mara D. Neusel
Mara.D.Neusel@ttu.edu
Abstract:
This is a survey article on degree bounds in invariant theory of finite
groups. A finite subgroup $G$ of the general linear group $\GL(n\, \F)$
over some field $\F$ acts via matrix multiplication on the vector space
$V=\F^n$. This induces an action of $G$ on the polynomials
$\F[x_1\commadots x_n]$ in $n$ variables. The polynomials
$\F[x_1\commadots x_n]^G\subseteq \F[x_1\commadots x_n]$ invariant under
this action form a subring. This ring is our center of study. In
particular we will discuss how to calculate this ring. In this context
degree bounds are central, and we want to present the known results. We
also sketch the techniques that are used to obtain good bounds and
describe open questions.
11.
http://hopf.math.purdue.edu/cgi-bin/generate?/Neusel-Wisniewski/piotr
Connected Hopf algebras with Dixmier bases and infinite primary
decomposition
Mara D. Neusel, Piotr Wisniewski
Mara.D.Neusel@ttu.edu pikonrad@mat.uni-torun.pl
Abstract:
In this paper we show the existence of invariant primary decompositions
in the categories of modules and rings over a Hopf algebra of Dixmier
type.
---------------------Instructions-----------------------------
To subscribe or unsubscribe to this list, send a message to Don Davis at
dmd1@lehigh.edu with your e-mail address and name.
Please make sure he is using the correct e-mail address for you.
To see past issues of this mailing list, point your WWW browser to
http://math.wesleyan.edu/~mhovey/archive/
If this doesn't work or is missing a few issues, try
http://www.lehigh.edu/~dmd1/algtop.html
which also has the other messages sent to Don's list.
To get the papers listed above, point your Web browser to the URL
listed. The general Hopf archive URL is
http://hopf.math.purdue.edu
There is a web form for submitting papers to Hopf on this site as well.
You should submit an abstract as well. Clarence has explicit
instructions for the form of this abstract: see
http://hopf.math.purdue.edu/new-html/submissions.html
In particular, your abstract is meant to be read by humans, so should be
as readable as possible. I reserve the right to edit unreadable
abstracts. You should then e-mail Clarence at wilker at math.purdue.edu
telling him what you have uploaded.
The largest archive of math preprints is at
http://arxiv.gov
There is an algebraic topology section in this archive. The most useful
way to browse it or submit papers to it is via the front end developed
by Greg Kuperberg:
http://front.math.ucdavis.edu
To get the announcements of new papers in the algebraic topology section
at the arXiv, send e-mail to math@arxiv.org with subject line "subscribe"
(without quotes), and with the body of the message "add AT" (without
quotes).
I am solely responsible for these messages---don't send complaints
about them to Clarence. Thanks to Clarence for creating and maintaining
the archive.