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An algebraic model for rational T2-equivariant elliptic cohomology
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Barucco, Matteo (2022) An algebraic model for rational T2-equivariant elliptic cohomology. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b3884222
Abstract
We construct a rational T2-equivariant elliptic cohomology theory for the 2-torus T2, starting from an elliptic curve C over C and a coordinate data around the identity. The theory is defined by constructing an object ECT2 in the algebraic model category dA(T2), which by Greenlees and Shipley [GS18] is Quillen-equivalent to rational T2-spectra. This result is a generalisation to the 2-torus of the construction [Gre05] for the circle T. The object ECT2 is directly built using geometric inputs coming from the Cousin complex of the structure sheaf of the complex abelian surface X = C × C. We use this construction to compute rational T-equivariant elliptic cohomology of CP(V ): the complex projective space of a finite dimensional complex representation V of T. More precisely we prove that ECT built in [Gre05] and ECT2 satisfy a split condition implying ECT(CP(V )+) _= ECT2(S(V w)+) where S(_) is the sphere of vectors with unit norm and w is the natural representation of T. The rational T2-elliptic cohomology of this space can be deduced from the one on spheres of complex representations SV of T2 that we compute in the construction of ECT2 .
Item Type: | Thesis (PhD) | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Curves, Elliptic, Homology theory, Algebraic topology, Abelian groups, Homotopy theory | ||||
Official Date: | April 2022 | ||||
Dates: |
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Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Greenlees, J. P. C. (John Patrick Campbell), 1959- | ||||
Format of File: | |||||
Extent: | vi, 128 pages | ||||
Language: | eng |
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