Holmstrom Elliptic cohomology

Elliptic cohomology

Two-vector bundles and forms of elliptic cohomology, by Nils A. Baas, Bjorn I. Dundas, and John Rognes: http://www.math.uiuc.edu/K-theory/0629

category: [Private] Notes


Elliptic cohomology

MathSciNet

Google Scholar

Google

arXiv: Experimental full text search

arXiv: Abstract search

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Elliptic cohomology

AT (Algebraic topology)

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Elliptic cohomology

Three articles on Hecke operators as operations on elliptic cohomology:

http://www.maths.gla.ac.uk/%7Eajb/dvi-ps/heckop.pdf

http://www.maths.gla.ac.uk/%7Eajb/dvi-ps/phecke.pdf

http://www.maths.gla.ac.uk/%7Eajb/dvi-ps/haell.pdf

Toen: Note of Chern character, loop spaces and derived algebraic geometry. File Toen web publ Abel-2007.pdf. Notion of derived cat sheaves, a categorification of the notion of complexes of sheaves of O-modules on schemes (also quasi-coh and perfect versions). Chern character for these categorical sheaves, a categorified version of the Chern char for perfect complexes with values in cyclic homology. Using the derived loop space. “This work can be seen as an attempt to define algebraic analogues of of elliptic objects and char classes for them”. 1. Motivations: Elliptic cohomology, geometric interpretations, chromatic level and n-categorical level, 2-VBs. Maybe the typical generalized CT of chromatic level n should be related to n-cats, more precisely cohom classes should be rep by maps from X to a certain n-stack. Rognes red-shift conjecture: Intuitively saying that the K-th spectrum of a commutative ring spectrum of chrom level n is of chrom level (n+1). More on ell cohom and 2-cats. Idea of categorical sheaves: For X a scheme, should have a symmetric monoidal 2-cat Cat(X) which is a categorification of Mod(X), in the sense that Mod(X) should be the cat of endomorphisms of the unit objects in Cat(X). More details. Notions of secondary cohomology and secondary K-theory. Notion of derived categorical sheaves, more reasonable than nonderived version. Relation between S 1S^1-equivariant functions on LX and negative cyclic homology. 2. Categorification of homological algebra and dg-cats. 3. Loop spaces in DAG. More, including relations with variations of Hodge structures. Final remark on algebraic elliptic cohomology. “Algebraic K-theory determines complex topological K-theory”, ref to Walker 2002.

Stable bundles over rig categories by Rognes et al, on 2-vector bundles.


Elliptic cohomology

The superb survey by Lurie. Also nlab discussion on this article.

Some nice slides of Strickland

http://ncatlab.org/nlab/show/elliptic+cohomology

http://nlab.mathforge.org/nlab/show/geometric+models+for+elliptic+cohomology

Folder: Elliptic cohomology, under AT


Elliptic cohomology

Miller and Ravenel, eds.

Also, at least one other recent book (~ 2007)

category: Paper References


Elliptic cohomology

http://mathoverflow.net/questions/101452/what-do-loop-groups-and-von-neumann-algebras-have-to-do-with-elliptic-cohomology

nLab page on Elliptic cohomology

Created on June 10, 2014 at 21:14:54 by Andreas Holmström