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arXiv · 1703.06562

Quasi-elliptic cohomology and its Spectrum

Zhen Huan
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Abstract

Ginzburg, Kapranov and Vasserot conjectured the existence of equivariant elliptic cohomology theories. In this paper, to give a description of equivariant spectra of the theories, we study an intermediate theory, quasi-elliptic cohomology. We formulate a new category of orthogonal G-spectra and construct explicitly an orthogonal G-spectrum of quasi-elliptic cohomology in it. The idea of the construction can be applied to a family of equivariant cohomology theories, including Tate K-theory and generalized Morava E-theories. Moreover, this construction provides a functor from the category of global spectra to the category of orthogonal G-spectra. In addition, from it we obtain some new idea what global homotopy theory is right for constructing global elliptic cohomology theory.

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Zhen Huan. 2017-03-20. Quasi-elliptic cohomology and its Spectrum. https://arxiv.org/abs/1703.06562

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