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Title Transchromatic generalized character maps
Publication Date
Date Accessioned
Degree PhD
Discipline/Department 0439
Degree Level doctoral
University/Publisher University of Illinois – Urbana-Champaign
Abstract In "Generalized Group Characters and Complex Oriented Cohomology Theories", Hopkins, Kuhn, and Ravenel discovered a generalized character theory that proved useful in studying cohomology rings of the form E^*(BG). In this paper we use the geometry of p-divisible groups to describe a sequence of "intermediate" character theories that retain more information about the cohomology theory E and yield the related result of Hopkins, Kuhn, and Ravenel as a special case.
Subjects/Keywords Algebraic Topology; Stable Homotopy Theory; Generalized Cohomology Theory; p-Divisible Group; Barsotti-Tate Group; Morava E-theory
Contributors Rezk, Charles (advisor); Ando, Matthew (Committee Chair); Rezk, Charles (committee member); McCarthy, Randy (committee member); Schenck, Henry K. (committee member)
Language en
Rights Copyright 2011 Nathaniel Stapleton
Country of Publication us
Record ID handle:2142/26269
Repository uiuc
Date Retrieved
Date Indexed 2020-03-09
Grantor University of Illinois at Urbana-Champaign
Issued Date 2011-08-25 22:21:33

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generalized cohomology theory on the category of finite spaces (spaces equivalent to a finite CW-complex), Topf . That is a functor (Topf )op −→ AB* from finite spaces to graded abelian groups that satisfies all of the Eilenberg-Steenrod…

…Hopkins, Kuhn, and Ravenel build, for each Morava E-theory, an equivariant cohomology theory that mimics the properties of Cl(G, L) and is the receptacle for a map from Borel equivariant En . They begin by constructing a ring L(En )…

…p-divisible group. Ct is flat over En0 and can X im α then for , G) and Fix(X) = be used to make a height t cohomology theory. Let Gp = hom(Zn−t p α∈Gp all finite G there is a map of equivariant theories En∗ (EG ×G X)…

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