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arXiv · 2205.09660

An algebraic model for rational $T^2$-equivariant elliptic cohomology

Matteo Barucco
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Abstract

We construct a rational $T^2$-equivariant elliptic cohomology theory for the 2-torus $T^2$, starting from an elliptic curve C over the complex numbers and a coordinate data around the identity. The theory is defined by constructing an object $EC_{T^2}$ in the algebraic model category $dA(T^2)$, which by Greenlees and Shipley is Quillen-equivalent to rational $T^2$-spectra. This result is a generalization to the 2-torus of the construction [Gre05] for the circle. The object $EC_{T^2}$ is directly built using geometric inputs coming from the Cousin complex of the structure sheaf of the surface CxC.

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Matteo Barucco. 2022-05-19. An algebraic model for rational $T^2$-equivariant elliptic cohomology. https://arxiv.org/abs/2205.09660

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