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Author
Title Transchromatic generalized character maps
URL
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)…

…character maps induce an isomorphism when the source is tensored up to Ct . 5 Chapter 2 Preliminaries 2.1 Conventions Within this paper all rings are commutative with unit and all graded rings are graded commutative. By a cohomology theory we mean a…

…axioms except for the dimension axiom. We choose finite spaces as our source category because it allows for flat extension of cohomology theories. By an equivariant cohomology theory we will always mean a Borel-equivariant theory. For G an abelian group…

…K(t)-theory for 0 ≤ t < n: LK(t) En . En is an even periodic height n theory and LK(t) En is an even periodic height t theory. Basic properties of these cohomology theories can be found in ([15], [6…

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