T. Schlank

activity

20092025

most citedThe

\infty

-Categorical Eckmann-Hilton Argument

33 citations · 137 across the 39 of their papers we have counts for

collaborators

48 papers

math.AG2025

Higher Zariski Geometry

Ko Aoki, Tobias Barthel, Anish Chedalavada +2

We revisit the classical constructions of tensor-triangular geometry in the setting of stably symmetric monoidal idempotent-complete $\infty$ -categories, henceforth referred to as…

cs.CL2024

Looking Beyond The Top-1: Transformers Determine Top Tokens In Order

Daria Lioubashevski, Tomer Schlank, Gabriel Stanovsky +1

Understanding the inner workings of Transformers is crucial for achieving more accurate and efficient predictions. In this work, we analyze the computation performed by Transformer…

math.NT2024

Arithmetic Kei Theory

Ariel Davis, Tomer M Schlank

A kei, or 2-quandle, is an algebraic structure one can use to produce a numerical invariant of links, known as coloring invariants. Motivated by Mazur's analogy between prime numbe…

math.AT2024

On Hopkins' Picard group

Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton +1

We compute the algebraic Picard group of the category of $K (n)$ -local spectra, for all heights $n$ and all primes $p$ . In particular, we show that it is always finitely generated o…

math.AT2024

On the rationalization of the $K (n)$ -local sphere

Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton +1

We compute the rational homotopy groups of the $K (n)$ -local sphere for all heights $n$ and all primes $p$ , verifying a prediction that goes back to the pioneering work of Morava in…

math.AT2023★ 1 cited

$K$ -theoretic counterexamples to Ravenel's telescope conjecture

Robert Burklund, Jeremy Hahn, Ishan Levy +1

At each prime $p$ and height $n + 1 \geq 2$ , we prove that the telescopic and chromatic localizations of spectra differ. Specifically, for $Z$ acting by Adams operations on $…

math.AT2023

Chromatic Cardinalities via Redshift

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank +1

Using higher descent for chromatically localized algebraic $K$ -theory, we show that the higher semiadditive cardinality of a $π$ -finite $p$ -space $A$ at the Lubin-Tate spectrum $E_…

math.KT2023★ 2 cited

Descent and cyclotomic redshift for chromatically localized algebraic K-theory

Shay Ben-Moshe, Shachar Carmeli, Tomer M. Schlank +1

We prove that $T (n + 1)$ -localized algebraic $K$ -theory satisfies descent for $π$ -finite $p$ -group actions on stable $\infty$ -categories of chromatic height up to $n$ , extending a re…

math.GT2023

The Hilbert Polynomial of Quandles and Colorings of Random Links

Ariel Davis, Tomer M. Schlank

Given a finite quandle $Q$ , we study the average number of $Q$ -colorings of the closure of a random braid in $B_{n}$ as $n$ varies. In particular we show that this number coincides w…

math.AT2022

The Chromatic Fourier Transform

Tobias Barthel, Shachar Carmeli, Tomer M. Schlank +1

We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n = 0$ , as well…

math.AT2022★ 6 cited

The Chromatic Nullstellensatz

Robert Burklund, Tomer M. Schlank, Allen Yuan

We show that Lubin--Tate theories attached to algebraically closed fields are characterized among $T (n)$ -local $E_{\infty}$ -rings as those that satisfy an analogue of Hilb…

math.AT2022★ 2 cited

The $\infty$ -Categorical Reflection Theorem and Applications

Shaul Ragimov, Tomer M. Schlank

We prove an $\infty$ -categorical version of the reflection theorem of Adámek-Rosický. Namely, that a full subcategory of a presentable $\infty$ -category which is closed under limit…

math.KT2021★ 14 cited

Higher Semiadditive Algebraic K-Theory and Redshift

Shay Ben-Moshe, Tomer M. Schlank

We define higher semiadditive algebraic K-theory, a variant of algebraic K-theory that takes into account higher semiadditive structure, as enjoyed for example by the $K (n)$ - and $…

math.AT2021

Evaluation maps and transfers for free loop spaces II

Sune Precht Reeh, Tomer M. Schlank, Nathaniel Stapleton

In our previous paper, we constructed and studied a functorial extension of the evaluation map $S^{1} \times L X \to X$ to transfers along finite covers. In this paper, we s…

math.AT2021

Evaluation maps and transfers for free loop spaces I

Sune Precht Reeh, Tomer M. Schlank, Nathaniel Stapleton

We construct and study a functorial extension of the evaluation map $S^{1} \times L X \to X$ to transfers along finite covers. For finite covers of classifying spaces of fi…

math.AT2021★ 6 cited

Chromatic Cyclotomic Extensions

Shachar Carmeli, Tomer M. Schlank, Lior Yanovski

We construct Galois extensions of the T(n)-local sphere, lifting all finite abelian Galois extensions of the K(n)-local sphere. This is achieved by realizing them as higher semiadd…

math.AT2021

Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra

Gregory Arone, Ilan Barnea, Tomer M. Schlank

In a companion paper [ABS1] we introduced the stable $\infty$ -category of noncommutative CW-spectra, which we denoted $NSp$ . Let $M$ denote the full spectrally e…

math.AT2021

Noncommutative CW-spectra as enriched presheaves on matrix algebras

Gregory Arone, Ilan Barnea, Tomer M. Schlank

Motivated by the philosophy that $C^{*}$ -algebras reflect noncommutative topology, we investigate the stable homotopy theory of the (opposite) category of $C^{*}$ -algebras. We focus on…

math.AT2020

Ambidexterity and Height

Shachar Carmeli, Tomer M. Schlank, Lior Yanovski

We introduce and study the notion of \emph{semiadditive height} for higher semiadditive $\infty$ -categories, which generalizes the chromatic height. We show that the higher semiadd…

math.NT2020★ 3 cited

Brauer and Etale Homotopy Obstructions to Rational Points on Open Covers

David Corwin, Tomer Schlank

In 2010, Poonen gave the first example of failure of the local-global principle that cannot be explained by Skorobogatov's étale Brauer-Manin obstruction. Motivated by this example…

math.AT2019★ 25 cited

Monochromatic homotopy theory is asymptotically algebraic

Tobias Barthel, Tomer M. Schlank, Nathaniel Stapleton

In previous work, we used an $\infty$ -categorical version of ultraproducts to show that, for a fixed height $n$ , the symmetric monoidal $\infty$ -categories of $E_{n, p}$ -local spect…

math.AT2019

On d-Categories and d-Operads

Tomer M. Schlank, Lior Yanovski

We extend the theory of d-categories, by providing an explicit description of the right mapping spaces of the d-homotopy category of an $\infty$ -category. Using this description, w…

math.AG2019★ 4 cited

Étale Homotopy Obstructions of Arithmetic Spheres

Edo Arad, Shachar Carmeli, Tomer M. Schlank

Let $K$ be a field of characteristic $\neq = 2$ and let $X$ be the affine variety over $K$ defined by the equation $X : a_{0} x_{0}^{2} + \dots + a_{n} x_{n}^{2} = 1$ where $n \geq 0$ and $a_i\i…

math.AG2018

Morphisms of rational motivic homotopy types

Ishai Dan-Cohen, Tomer Schlank

We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphism…

Higher Zariski Geometry

Looking Beyond The Top-1: Transformers Determine Top Tokens In Order

Arithmetic Kei Theory

On Hopkins' Picard group

On the rationalization of the K(n)-local sphere

K-theoretic counterexamples to Ravenel's telescope conjecture

Chromatic Cardinalities via Redshift

Descent and cyclotomic redshift for chromatically localized algebraic K-theory

The Hilbert Polynomial of Quandles and Colorings of Random Links

The Chromatic Fourier Transform

The Chromatic Nullstellensatz

The ∞-Categorical Reflection Theorem and Applications

Higher Semiadditive Algebraic K-Theory and Redshift

Evaluation maps and transfers for free loop spaces II

Evaluation maps and transfers for free loop spaces I

Chromatic Cyclotomic Extensions

Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra

Noncommutative CW-spectra as enriched presheaves on matrix algebras

Ambidexterity and Height

Brauer and Etale Homotopy Obstructions to Rational Points on Open Covers

Monochromatic homotopy theory is asymptotically algebraic

On d-Categories and d-Operads

Étale Homotopy Obstructions of Arithmetic Spheres

Morphisms of rational motivic homotopy types

On the rationalization of the $K (n)$ -local sphere

$K$ -theoretic counterexamples to Ravenel's telescope conjecture

The $\infty$ -Categorical Reflection Theorem and Applications