Subject: new Hopf listings
Date: 17 Oct 2001 14:33:14 -0400
From: Mark Hovey
There are 2 new papers on Hopf this tiem.
Mark Hovey
New papers appearing on hopf between 9/17/01 and 10/17/01
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Dwyer-Isaksen/obstruction
Obstruction theory in model categories
J. Daniel Christensen, William G. Dwyer and Daniel C. Isaksen
MSC: 55S35, 55U35, 18G55 (primary); 18G30, 55P42 (secondary)
Department of Mathematics
University of Western Ontario
London, Ontario N6A 5B7
jdc@uwo.ca
Department of Mathematics
University of Notre Dame
South Bend, IN 46556
dwyer.1@nd.edu
Department of Mathematics
University of Notre Dame
South Bend, IN 46556
isaksen.1@nd.edu
Keywords: obstruction theory, closed model category, simplicial set,
spectrum
Working in an arbitrary pointed proper model category, we describe the
cofibrations that have an obstruction theory with respect to all
fibrations. Up to weak equivalence, retract, and cobase change, they
are the cofibrations with weakly contractible target. Equivalently,
they are the retracts of principal cofibrations. Without properness,
the same classification holds for cofibrations with cofibrant source.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Toen-Vezzosi/agmod-web
Title: Algebraic Geometry over model categories (a general approach to
derived algebraic geometry)
Authors: Bertrand Toen and Gabriele Vezzosi
AMS Classification numbers: 14A20; 18G55; 55P43; 55U40;18F10
Submitted to the xxxLANL as math.AG/0110109, October 10, 2001
Addresses of authors: Bertrand Toen, Laboratoire J. A. Dieudonne,
UMR CNRS 6621, Universite' de Nice-Sophia Antipolis, France.
toen@math.unice.fr
Gabriele Vezzosi, Diprtimento di Matematica, Universita'
di Bologna, Italy,
vezzosi@dm.unibo.it
Included gzipped .ps file
ABSTRACT: For a (semi-)model category M, we define a notion of a
''homotopy'' Grothendieck topology on M, as well as its
associated model category of stacks. We use this to define a
notion of geometric stack over a symmetric monoidal base model
category; geometric stacks are the fundamental objects to "do
algebraic geometry over model categories". We give two examples of
applications of this formalism. The first one is the
interpretation of DG-schemes as geometric stacks over the model
category of complexes and the second one is a definition of
etale K-theory of E_{\infty}-ring spectra.
This first version is very preliminary and might be considered as
a detailed research announcement. Some proofs, more details and
more examples will be added in a forthcoming version.
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