Lubin-Tate theory, character theory, and power operations
Nathaniel Stapleton
TL;DR
This paper explores the interplay between Lubin-Tate deformation theory, character theory, and power operations in chromatic homotopy theory, providing new formulas for E-cohomology of finite groups.
Contribution
It introduces moduli problems related to Lubin-Tate theory and uses symmetries with character theory to derive formulas for power operations.
Findings
Formulas for power operations in E-cohomology
Descriptions of symmetries in moduli problems
Connections between deformation theory and character theory
Abstract
This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their symmetries. These symmetries are then used in conjunction with the Hopkins-Kuhn-Ravenel character theory to provide formulas for the power operations and the stabilizer group action on the E-cohomology of a finite group.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra