Anderson and Gorenstein duality
@article{Greenlees2016AndersonAG, title={Anderson and Gorenstein duality}, author={John Greenlees and Vesna Stojanoska}, journal={arXiv: Algebraic Topology}, year={2016} }
The paper relates the Gorenstein duality statements studied by the first author to the Anderson duality statements studied by the second author, and explains how to use local cohomology and invariant theory to understand the numerology of shifts in simple cases.
4 Citations
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References
SHOWING 1-10 OF 23 REFERENCES
Brown-Comenetz duality and the Adams spectral sequence
- Mathematics
- 1999
<abstract abstract-type="TeX"><p>We show that the class of <i>p</i>-complete connective spectra with finitely presented cohomology over the Steenrod algebra admits a duality theory related to…
Gross-Hopkins duality and the Gorenstein condition
- Mathematics
- 2009
Gross and Hopkins have proved that in chromatic stable homotopy, Spanier-Whitehead duality nearly coincides with Brown-Comenetz duality. Our goal is to give a conceptual interpretation for this…
K-theory, reality, and duality
- Mathematics
- 2014
We present a new proof of Anderson's result that the real K -theory spectrum is Anderson self-dual up to a fourfold suspension shift; more strongly, we show that the Anderson dual of the complex K…
Gorenstein duality for Real spectra
- Mathematics
- 2016
Following Hu and Kriz, we study the $C_2$-spectra $BP\mathbb{R}\langle n \rangle$ and $E\mathbb{R}(n)$ that refine the usual truncated Brown-Peterson and the Johnson-Wilson spectra. In particular, we…
Duality in algebra and topology
- Mathematics
- 2006
We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré…
Topological Modular Forms of Level 3
- Mathematics
- 2008
We describe and compute the homotopy of spectra of topological modular forms of level 3. We give some computations related to the "building complex" associated to level 3 structures at the prime 2.…
THE SHIMURA CURVE OF DISCRIMINANT 15 AND TOPOLOGICAL AUTOMORPHIC FORMS
- MathematicsForum of Mathematics, Sigma
- 2015
We find defining equations for the Shimura curve of discriminant 15 over $\mathbb{Z}[1/15]$. We then determine the graded ring of automorphic forms over the 2-adic integers, as well as the higher…
Duality for Topological Modular Forms
- Mathematics
- 2011
It has been observed that certain localizations of the spectrum of topological modular forms are self-dual (Mahowald-Rezk, Gross-Hopkins). We provide an integral explanation of these results that is…