I am a second year PhD student at the Copenhagen Centre for Geometry and Topology.
My advisors are Robert Burklund and Jesper Grodal.
I am interested in all things stable homotopy theory and higher algebra.

You can reach/find me at:

email: florian dot riedel at pm dot me
office: 04.4.03

My pronouns are he/him.
If you write to me, feel free to call me Florian or Flo.

My CV as of 21.08.25: CV

Preprints

  1. Reduced and geometric points of E_∞-rings in positive characteristic [arxiv link] We investigate whether an arbitrary non-zero E_∞-ring $A$ admits a reduced point, meaning an E_∞-map $A\to T$ such that $\pi_{\ast}T$ is a graded field. We show that if $2\in \pi_{0}A$ is not invertible, then $A$ admits a reduced point and as an application deduce that a free $A$-module on $n$ generators cannot be built from $n-1$ many cells. Perhaps surprisingly, the existence of reduced points completely fails at odd primes. More precisely, for any prime $p>2$, we construct a non-zero E_∞-ring over $\mathbb{F}_{p}$ which admits no map to an E_2-algebra $T$ such that $\pi_{0}T$ is a field.
  2. On the K-Theory of algebraic tori (joint with Bai, Carmeli and Juran; [img]) [arxiv link] (submitted) Given an algebraic torus $T$ over a field $F$, its lattice of characters $\Lambda$ gives rise to a topological torus $\mathfrak{T}(T)=\Lambda_{\mathbb R}/\Lambda$ with a continuous action of the absolute Galois group $G$. We construct a natural equivalence between the algebraic $K$-theory $K_{\ast}(T)$ and the equivariant homology $H^{G}_{\ast}(\mathfrak{T}(T);K_G(F))$ of the topological torus $\mathfrak{T}(T)$ with coefficients in the $G$-equivariant $K$-theory of $F$. This generalizes a computation of $K_0(T)$ due to Merkurjev and Panin. We obtain this equivalence by analyzing the motive $\mathbb{K}_{F}^{T}$ in the stable motivic category $\mathrm{SH}(F)$ of Voevodsky and Morel, where $\mathbb{K}_{F}$ is the motivic spectrum representing homotopy $K$-theory. We construct a natural comparison map $\mathfrak{F}\colon \mathbb{K}_{F}[B\Lambda] \to \mathbb{K}_{F}^{T}$ from the $\mathbb{K}_{F}$-homology of the \'etale delooping of $\Lambda$ to $\mathbb{K}_{F}^{T}$ as a special case of a motivic Fourier transform and prove that it is an equivalence by using a motivic Eilenberg--Moore formula for classifying spaces of tori.
  3. On the deformation theory of E_∞-coalgebras [arxiv link] (submitted) We introduce a notion of formally étale E_∞-coalgebras and show that they admit essentially unique, functorial lifts along square zero extensions of E_∞-rings. Using this, we show that for a perfect $\mathbb{F}_{p}$-algebra $k$, Weil restriction along the augmentation $\mathbb{W}(k)\to k$ induces a fully faithful functor from formally étale, connective E_∞-coalgebras in $k$-modules to connective E_∞-coalgebras in $p$-complete modules over the spherical Witt vectors $\mathbb{W}(k)$. Finally, we prove that for any connected space $X$, the $k$-homology $k[X]$ is a formally étale E_∞-coalgebra in $k$-modules. This shows that $\mathbb{W}(k)[X]^{\wedge}_p$ can be recovered as the essentially unique lift of $k[X]$ to a connective coalgebra in $p$-complete $\mathbb{W}(k)$-modules.

Other writing

Expository material and notes.

The rationalization of the K(n)-local sphere pdf
Notes for a talk I gave in the Topics in Topology seminar at KU.

Galois categories and the étale fundamental group pdf
A lightly edited version of my bachelor thesis.

Topological Cyclic Homology pdf
My notes on THH, TC and friends for the popular TV-series.