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. ---------------------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://www.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 WWW client (Netscape< Internet Explorer) to the URL listed. The general Hopf archive URL is http://hopf.math.purdue.edu There are links to Purdue seminars, and other math related things on this page as well. The largest archive of math preprints is at http://xxx.lanl.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 xxx, send e-mail to math@xxx.lanl.gov with subject line "subscribe" (without quotes), and with the body of the message "add AT" (without quotes). You can also access Hopf through ftp. Ftp to hopf.math.purdue.edu, and login as ftp. Then cd to pub. Files are organized by author name, so papers by me are in pub/Hovey. If you want to download a file using ftp, you must type binary before you type get . To put a paper of yours on the archive, cd to /pub/incoming. Transfer the dvi file using binary, by first typing binary then put You should also transfer 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@math.purdue.edu telling him what you have uploaded. I am solely responsible for these messages---don't send complaints about them to Clarence. Thanks to Clarence for creating and maintaining the archive.