Elliptic loop spaces
Emile Bouaziz, Adeel A. Khan

TL;DR
This paper introduces an elliptic analogue of loop spaces in derived algebraic geometry, expanding the classical rational and trigonometric cases to include elliptic objects, and explores their categorical and cohomological properties.
Contribution
It defines an elliptic loop space as a stack of maps from an exotic elliptic curve avatar, completing the classical trichotomy and linking to equivariant elliptic Hodge cohomology.
Findings
Defines the elliptic loop space in derived algebraic geometry.
Establishes a connection to equivariant elliptic Hodge cohomology.
Completes the trichotomy of rational, trigonometric, and elliptic objects.
Abstract
We introduce an elliptic avatar of loop spaces in derived algebraic geometry, completing the familiar trichotomoy of rational, trigonometric and elliptic objects. Heuristically, the elliptic loop space of is the stack of maps to from a certain exotic avatar of the elliptic curve , such that the category of quasi-coherent sheaves on is the convolution category of zero-dimensionally supported coherent sheaves on . For quotient stacks, the structure sheaf of the elliptic loop space gives rise to a theory of equivariant elliptic Hodge cohomology.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · Algebraic and Geometric Analysis
