PhD defence by Florian Matthias Riedel

Two interactions between stable homotopy theory and geometry

PhD defence by Florian Matthias Riedel

Assessment Committee

Professor Nathalie Wahl, Math, University of Copenhagen (Chairperson)
Associate Professor Achim Krause, University of Olso
Tenure track assistant professor Elden Elmanto, University of Toronto

Supervisors

Professor Jesper Kragh Grodal
Associate Professor Robert Wayne Burklund

Department

Department of Mathematical Sciences

Place

Building: HC Ørsted Institut, Room: Auditorium 4, Universitetsparken 5, 2100 Copenhagen

Email address to gain access to the thesis: florian.riedel@pm.me.
You will either receive a copy of the thesis or be informed where you can read a physical copy.
Recipients of copies of the thesis are not allowed to share or distribute it due to copyright compliance.

Short description of the thesis

This thesis consists of two papers, both 
exploring different aspects of the interaction of stable homotopy theory
and geometry.

The first is about spectral algebraic geometry in positive
characteristic. We discuss different notions of points of E∞-rings
over a finite field and find that nilpotent classes play a fundamentally
different role, depending on whether the characteristic is odd or even.

The second studies the motivic E∞-ring representing algebraic 
K-theory of smooth schemes. We construct a kind of Fourier transform
for this ring, which in particular witnesses that the category of
representations of an algebraic torus is semi-simple. Using this, 
we give a formula for the K-theory of an algebraic torus as
the equivariant homology of its topological mirror.