Cyclotomic Spectra and Topological Cyclic Homology of $\E_\infty$-Ring Spectra

Specialeforsvar ved Anders Jess Pedersen

Titel: Cyclotomic Spectra and Topological Cyclic Homology of $\E_\infty$-Ring Spectra

  

Abstract: This thesis introduces $\E_\infty$-ring spectra and cyclotomic spectra and their invariants topological Hochschild homology and topological cyclic homology respectively. The thesis is divided into four chapters: In the first we introduce the necessary $\infty$-categorical prerequisites. In the second we introduce the theory of symmetric monoidal $\infty$-categories, a $K$-theory machine analogous to Segals infinite loop space machine, and lastly topological Hochschild homology. In the third part we introduce the Tate construction and the Tate diagonal. In the last part we introduce different versions of cyclotomic spectra, and show in which cases these coincide

 

Vejleder:  Markus Hausmann
Censor:     Iver M. Ottosen, Aalborg Universitetet