Subject: new Hopf listings
From: Mark Hovey
Date: 05 Nov 2006 09:09:17 -0500
There are 4 new papers this time, from Chebolu-Christensen-Minac,
DavisDaniel, Stacey-Whitehouse, and Yagita.
Mark Hovey
New papers appearing on hopf between 10/6/06 and 11/5/06
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Chebolu-Christensen-Minac/GH-StMod
TITLE: Groups which do not admit ghosts
AUTHORS: Sunil K. Chebolu, J. Daniel Christensen, and Jan Minac
Department of Mathematics
University of Western Ontario
London, ON N6A 5B7, Canada
AMS Subject classsification: Primary 20C20, 20J06; Secondary 55P42
ABSTRACT: A ghost in the stable module category of a group G is a map
between
representations of G that is invisible to Tate cohomology. We show that
the
only non-trivial finite p-groups whose stable module categories have no
non-trivial ghosts are the cyclic groups of order 2 and 3. We compare this
to
the situation in the derived category of a commutative ring.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/DavisDaniel/siterplusg
Title: The site R^+_G for a profinite group G
Author: Daniel G. Davis
AMS classification number: 55P42, 55U35, 18B25
Abstract: Let G be a non-finite profinite group and let
G-Sets_{df} be the canonical site of finite discrete
G-sets. Then the category R^+_G, defined by Devinatz and
Hopkins, is the category obtained by considering G-Sets_{df}
together with the profinite G-space G itself, with morphisms
being continuous G-equivariant maps. We show that R^+_G
is a site when equipped with the pretopology of epimorphic
covers. Also, we explain why the associated topology on R^+_G
is not subcanonical, and hence, not canonical. We note that,
since R^+_G is a site, there is automatically a model category
structure on the category of presheaves of spectra on the
site. Finally, we point out that such presheaves of spectra
are a nice way of organizing the data that is obtained by
taking the homotopy fixed points of a continuous G-spectrum
with respect to the open subgroups of G.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Stacey-Whitehouse/deloopv2
Title: Stable and Unstable Operations in mod p Cohomology Theories
Authors: Andrew Stacey and Sarah Whitehouse
AMS classification number: 55S25, 55P47
Other useful information: math.AT/0605471
Abstract:
We consider operations between two multiplicative, complex orientable
cohomology theories. Under suitable hypotheses, we construct a map
from unstable to stable operations, left-inverse to the usual map from
stable to unstable operations. In the main example, where the target
theory is one of the Morava K-theories, this provides a simple and
explicit description of a splitting arising from the Bousfield-Kuhn
functor.
This is an updated version of an earlier submission. The proof of
proposition 3.2 has been corrected; other minor improvements have been
made.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/Yagita/abp
Algebraic BP-theory and norm varieties
Nobuaki Yagita
Department of Mathematics, Faculty of Education, Ibaraki University,
Mito, Ibaraki, Japan
Primary 14C15, 57T25; Secondary 55R35, 57T05
Let X be a smooth variety over a field k of characteristic zero. For a
fixed prime p, the algebraic BP-theory ABP(X) is the algebraic version
of the topological BP-theory. Given a nonzero symbol
a in K_{n+1}^M (k)/p,
the norm variety V_a is a variety such that a=0 in K_{n+1}^M (k(V_a))/p
and V_a(C)=v_n. In this paper, we mainly study ABP(V_a) for p an odd
prime.
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