An algebraic model for rational T²-equivariant elliptic cohomology

2022/05/19 by Barucco, Matteo
#13D45 #14B15 #14F06 (Secondary) #55N20 #55N34 #55N91 (Primary) 14H52 #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.09660

Abstract

We construct a rational T²-equivariant elliptic cohomology theory for the 2-torus T², 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_T² in the algebraic model category dA(T²), which by Greenlees and Shipley is Quillen-equivalent to rational T²-spectra. This result is a generalization to the 2-torus of the construction [Gre05] for the circle. The object EC_T² is directly built using geometric inputs coming from the Cousin complex of the structure sheaf of the surface CxC.

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