The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory

Announcement the Rigid Analytic Period Mapping , Lubin - Tate Space , and Stable Homotopy Theory

The geometry of the Lubin-Tate space of deformations of a formal group is studied via anétale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory.

The Rigid Analytic Period Mapping, Lubin-tate Space, and Stable Homotopy Theory

The geometry of the Lubin-Tate space of deformations of a formal group is studied via an étale, rigid analytic map from the deformation space to projective space. This leads to a simple description of the equivariant canonical bundle of the deformation space which, in turn, yields a formula for the dualizing complex in stable homotopy theory. Introduction Ever since Quillen [22, 1 ] discovered ...

Lubin-Tate Theory

Motivation: We seek to understand the stable homotopy category by understanding the structure of the moduli stack of formal groups. Over algebraically closed fields, this is straightforward. If char(k) = 0, every formal group law is isomorphic to the additive one and we’ve described the group of automorphisms (coordinates changes) before. If char(k) = p > 0 every formal group law is classified ...

The Lubin-tate Spectrum and Its Homotopy Fixed Point Spectra

This note is a summary of the results of my Ph.D. thesis (plus slight modifications), completed May 9, 2003, under the supervision of Professor Paul Goerss at Northwestern University. Let En be the Lubin-Tate spectrum with En∗ = W (Fpn)[[u1, ..., un−1]][u], where the degree of u is −2 and the complete power series ring over the Witt vectors is in degree zero. Let Gn = Sn o Gal(Fpn/Fp), where Sn...

Tate Cohomology in Axiomatic Stable Homotopy Theory