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. 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