Maxime Ramzi

activity

20202026

most citedA multiplicative comparison of MacLane homology and topological Hochschild homology

3 citations · 10 across the 24 of their papers we have counts for

collaborators

27 papers

math.CT2026

Cocompactness and Presentability

Thorger Geiß, Phil Pützstück, Maxime Ramzi

We give a short proof that $κ$ -cocompact objects in a presentable category are subterminal. As our main result, we extend this to the setting of presentable $\infty$ -categories. A…

math.KT2026

$Mot^{loc}$ is not compactly generated

Maxime Ramzi

We prove that the $\infty$ -category of localizing motives in the sense of Blumberg--Gepner--Tabuada is not compactly generated, extending a result of Efimov.

math.AT2026

The Galois theory of $G$ -spectra and the Burnside ring

Niko Naumann, Luca Pol, Maxime Ramzi

We prove that the Galois groupoid of the category of $G$ -spectra for a finite group $G$ is algebraic, i.e. equivalent to the étale fundamental groupoid of the Burnside ring of $G$ .…

math.KT2026

Chromatic Noshift

Maxime Ramzi

The chromatic redshift philosophy, introduced by Ausoni and Rognes, suggests that algebraic $K$ -theory raises chromatic height by $1$ . We show that the analogue of this philosophy…

math.CT2026

Free rigid commutative algebras

Maxime Ramzi

We describe free rigid commutative algebras in $2$ -presentably symmetric monoidal $(\infty, 2)$ -categories as oplax colimits over the $1$ -dimensional framed cobordism category. The…

math.AT2026

Geometric Points in Tensor Triangular Geometry

Tobias Barthel, Logan Hyslop, Maxime Ramzi

In this paper, we study geometric points in tensor triangular geometry. In doing so, we construct a counter-example to Balmer's Nerves of Steel conjecture using free constructions…

math.KT2026

Equivariant localizing motives and multiplicative norms on algebraic K-theory

Kaif Hilman, Maxime Ramzi

We construct multiplicative norms on equivariant nonconnective algebraic $K$ -theory for finite groups $G$ . We also construct a genuine equivariant version of THH equipped with a De…

math.KT2025

$K (1)$ -local $K$ -theory of Azumaya algebras

Maxime Ramzi

We compute certain strict Picard spectra of $K (1)$ -local $K$ -theory spectra of schemes in terms of Brauer groups, using the map that takes an Azumaya algebra to its $K (1)$ -local $K…

math.AG2025

Localizing motives of Azumaya algebras

Maxime Ramzi

We prove that the natural map from the derived Brauer group of a qcqs scheme $X$ to the Picard group of $X$ -linear motives is injective, extending results of Tabuada and Tabuada-Va…

math.KT2025

$p$ -perfection and group completion of $E_{\infty}$ -monoids

Maxime Ramzi, Maria Yakerson

We study $E_{\infty}$ -monoids on which a prime $p$ acts invertibly, which we call $p$ -perfect, in the non-group-complete situation. In particular, we prove that in many exam…

math.KT2025

Every motive is the motive of a stable $\infty$ -category

Maxime Ramzi, Vladimir Sosnilo, Christoph Winges

We define a class of motivic equivalences of small stable $\infty$ -categories $W_{mot}$ and show that the Dwyer--Kan localization functor $\mathrm{Cat}^{\mathrm{perf}}_\in…

math.AT2025

On endomorphisms of topological Hochschild homology

Maxime Ramzi

We compute endomorphisms of topological Hochschild homology ( $THH$ ) as a functor on stable $\infty$ -categories, as well as variants thereof: we also compute endomorphisms…

math.CT2025

Fully faithful functors and pushouts of $\infty$ -categories

Peter J. Haine, Maxime Ramzi, Jan Steinebrunner

We study stability properties of fully faithful functors, and compute mapping anima in pushouts of $\infty$ -categories along fully faithful functors. We provide applications of the…

math.AT2025★ 1 cited

Universality of Barwick's unfurling construction

Bastiaan Cnossen, Tobias Lenz, Maxime Ramzi

Given an $\infty$ -category $C$ with pullbacks, its $(\infty, 2)$ -category $Span (C)$ of spans has the universal property of freely adding right adjoints…

math.AT2024

A symmetric monoidal fracture square

Niko Naumann, Luca Pol, Maxime Ramzi

Given a symmetric monoidal stable $\infty$ -category $C$ which is rigidly-compactly generated and a set of compact objects $K$ of $C$ , one can form the…

math.AT2024

Separable commutative algebras in equivariant homotopy theory

Niko Naumann, Luca Pol, Maxime Ramzi

Given a finite group $G$ and a commutative ring $G$ -spectrum $R$ , we study the separable commutative algebras in the category of compact $R$ -modules. We isolate three conditions on…

math.CT2024

Dualizable presentable $\infty$ -categories

Maxime Ramzi

We prove that for any presentably symmetric monoidal $\infty$ -category $V$ , the $\infty$ -category $Mod_{V} (Pr^{L})^{dbl}$ of d…

math.CT2024

Locally rigid $\infty$ -categories

Maxime Ramzi

We develop the theory of locally rigid and rigid symmetric monoidal $\infty$ -categories over an arbitrary base $V \in CAlg (Pr^{L})$ . Among other th…

math.KT2024

Every spectrum is the K-theory of a stable $\infty$ -category

Maxime Ramzi, Vladimir Sosnilo, Christoph Winges

We prove that any spectrum is equivalent to the nonconnective K-theory of a stable $\infty$ -category. We use these results to construct a stable $\infty$ -category $C$ wit…

math.AC2023

A note on quadratic forms

Fabian Hebestreit, Achim Krause, Maxime Ramzi

For a field extension $L / K$ we consider maps that are quadratic over $L$ but whose polarisation is only bilinear over $K$ . Our main result is that all such are automatically quadra…

math.AT2023★ 2 cited

Separability in homotopical algebra

Maxime Ramzi

We study the notion of \emph{separable algebras} in the context of symmetric monoidal stable $\infty$ -categories. In the first part of this paper, we compare this context to that o…

math.AT2022★ 1 cited

On the multiplicativity of the Euler characteristic

John R. Klein, Cary Malkiewich, Maxime Ramzi

In this short paper, we give two proofs that the Euler characteristic is multiplicative, for fiber sequences of finitely dominated spaces. This is equivalent to proving that the Be…

math.AT2022★ 2 cited

Characters and transfer maps via categorified traces

Shachar Carmeli, Bastiaan Cnossen, Maxime Ramzi +1

We develop a theory of generalized characters of local systems in $\infty$ -categories, which extends classical character theory for group representations and, in particular, the in…

math.CT2022

An elementary proof of the naturality of the Yoneda embedding

Maxime Ramzi

We give a short proof that the Yoneda embedding is natural for $\infty$ -categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embe…

Cocompactness and Presentability

Motloc is not compactly generated

The Galois theory of G-spectra and the Burnside ring

Chromatic Noshift

Free rigid commutative algebras

Geometric Points in Tensor Triangular Geometry

Equivariant localizing motives and multiplicative norms on algebraic K-theory

K(1)-local K-theory of Azumaya algebras

Localizing motives of Azumaya algebras

p-perfection and group completion of E∞​-monoids

Every motive is the motive of a stable ∞-category

On endomorphisms of topological Hochschild homology

Fully faithful functors and pushouts of ∞-categories

Universality of Barwick's unfurling construction

A symmetric monoidal fracture square

Separable commutative algebras in equivariant homotopy theory

Dualizable presentable ∞-categories

Locally rigid ∞-categories

Every spectrum is the K-theory of a stable ∞-category

A note on quadratic forms

Separability in homotopical algebra

On the multiplicativity of the Euler characteristic

Characters and transfer maps via categorified traces

An elementary proof of the naturality of the Yoneda embedding

$Mot^{loc}$ is not compactly generated

The Galois theory of $G$ -spectra and the Burnside ring

$K (1)$ -local $K$ -theory of Azumaya algebras

$p$ -perfection and group completion of $E_{\infty}$ -monoids

Every motive is the motive of a stable $\infty$ -category

Fully faithful functors and pushouts of $\infty$ -categories

Dualizable presentable $\infty$ -categories

Locally rigid $\infty$ -categories

Every spectrum is the K-theory of a stable $\infty$ -category