Robert Burklund

activity

20192026

A^{1}

-degree

7 citations · 28 across the 19 of their papers we have counts for

collaborators

20 papers

math.AG2026

Inaccessibility of the flat topology

Ko Aoki, Robert Burklund

We prove that singleton covers in the flat topology on affine schemes are not closed under $κ$ -cofiltered limits for any regular cardinal $κ$ . Therefore, for every accessible flat…

math.AG2026

Motivic Hochschild homology of mod 2 motivic cohomology over algebraically closed fields

Tom Bachmann, Robert Burklund, Bjørn Ian Dundas +1

We compute the tensor of the multiplicative group scheme with the mod- $2$ motivic cohomology spectrum in normed motivic spectra over the complex numbers, and find that the resultin…

math.AG2025

Motivic stable stems and Galois approximations of cellular motivic categories

Tom Bachmann, Robert Burklund, Zhouli Xu

We reconstruct (appropriately completed) categories of cellular motivic spectra over fields of small cohomological dimension in terms of only their absolute Galois groups. As our m…

math.AT2024

Classical stable homotopy groups of spheres via $F_{2}$ -synthetic methods

Robert Burklund, Daniel C. Isaksen, Zhouli Xu

We study the $F_{2}$ -synthetic Adams spectral sequence. We obtain new computational information about $C$ -motivic and classical stable homotopy groups.

math.AT2024

A note on the Segal conjecture for large objects

Robert Burklund, Vignesh Subramanian

The Segal conjecture for $C_{p}$ (as proved by Lin and Gunawardena) asserts that the canonical map from the $p$ -complete sphere spectrum to the Tate construction for the trivial acti…

math.AT2024

$E_{\infty}$ -coalgebras and $p$ -adic homotopy theory

Tom Bachmann, Robert Burklund

We show that for any separably closed field $k$ of characteristic $p > 0$ , the canonical functor from nilpotent $p$ -adic spaces to $E_{\infty}$ -coalgebras over $k$ (given by…

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

Quivers and the Adams spectral sequence

Robert Burklund, Piotr Pstrągowski

In this paper, we describe a novel way of identifying Adams spectral sequence $E_{2}$ -terms in terms of homological algebra of quiver representations. Our method applies much more br…

math.AT2023

The Adams differentials on the classes $h_{j}^{3}$

Robert Burklund, Zhouli Xu

In filtration 1 of the Adams spectral sequence, using secondary cohomology operations, Adams computed the differentials on the classes $h_{j}$ , resolving the Hopf invariant one probl…

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★ 1 cited

Multiplicative structures on Moore spectra

Robert Burklund

In this article we show that $S /8$ is an $E_{1}$ -algebra, $S /32$ is an $E_{2}$ -algebra, $S / p^{n + 1}$ is an $E_{n}$ -algebra at odd pri…

math.AT2022★ 1 cited

How Big are the Stable Homotopy Groups of Spheres?

Robert Burklund, Andrew Senger

In this article we show that the $p$ -torsion exponent of the stable stems grows sublinearly in $n$ and the $p$ -rank of the $E_{2}$ -page of the Adams spectral sequence grows as $\exp(…

math.AT2022

Adams-type maps are not stable under composition

Robert Burklund, Ishan Levy, Piotr Pstrągowski

We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite…

math.KT2021

On the K-theory of regular coconnective rings

Robert Burklund, Ishan Levy

We show that for a coconnective ring spectrum satisfying regularity and flatness assumptions, its algebraic K-theory agrees with that of its $π_{0}$ . We prove this as a consequence o…

math.AT2020★ 1 cited

Galois reconstruction of Artin-Tate $R$ -motivic spectra

Robert Burklund, Jeremy Hahn, Andrew Senger

We explain how to reconstruct the category of Artin-Tate $R$ -motivic spectra as a deformation of the purely topological $C_{2}$ -equivariant stable category. The special fibe…

math.GT2020

Inertia groups in the metastable range

Robert Burklund, Jeremy Hahn, Andrew Senger

We prove that the inertia groups of all sufficiently-connected, high-dimensional $(2 n)$ -manifolds are trivial. This is a key step toward a general classification of manifolds in th…

math.AT2020★ 6 cited

On the high-dimensional geography problem

Robert Burklund, Andrew Senger

In 1962, Wall showed that smooth, closed, oriented, $(n - 1)$ -connected $2 n$ -manifolds of dimension at least $6$ are classified up to connected sum with an exotic sphere by an algebr…

math.AT2020★ 4 cited

An extension in the Adams spectral sequence in dimension 54

Robert Burklund

We establish a hidden extension in the Adams spectral sequence converging to the stable homotopy groups of spheres at the prime 2 in the 54-stem. This extension is exceptional in t…

math.AT2019★ 7 cited

The trace of the local $A^{1}$ -degree

Thomas Brazelton, Robert Burklund, Stephen McKean +2

We prove that the local $A^{1}$ -degree of a polynomial function at an isolated zero with finite separable residue field is given by the trace of the local $A^{1}$ -deg…

math.AT2019★ 1 cited

On the boundaries of highly connected, almost closed manifolds

Robert Burklund, Jeremy Hahn, Andrew Senger

Building on work of Stolz, we prove for integers $0 \leq d \leq 3$ and $k > 232$ that the boundaries of $(k - 1)$ -connected, almost closed $(2 k + d)$ -manifolds also bound parallelizable ma…

Inaccessibility of the flat topology

Motivic Hochschild homology of mod 2 motivic cohomology over algebraically closed fields

Motivic stable stems and Galois approximations of cellular motivic categories

Classical stable homotopy groups of spheres via F2​-synthetic methods

A note on the Segal conjecture for large objects

E∞​-coalgebras and p-adic homotopy theory

K-theoretic counterexamples to Ravenel's telescope conjecture

Quivers and the Adams spectral sequence

The Adams differentials on the classes hj3​

The Chromatic Nullstellensatz

Multiplicative structures on Moore spectra

How Big are the Stable Homotopy Groups of Spheres?

Adams-type maps are not stable under composition

On the K-theory of regular coconnective rings

Galois reconstruction of Artin-Tate R-motivic spectra

Inertia groups in the metastable range

On the high-dimensional geography problem

An extension in the Adams spectral sequence in dimension 54

The trace of the local A1-degree

On the boundaries of highly connected, almost closed manifolds

Classical stable homotopy groups of spheres via $F_{2}$ -synthetic methods

$E_{\infty}$ -coalgebras and $p$ -adic homotopy theory

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

The Adams differentials on the classes $h_{j}^{3}$

Galois reconstruction of Artin-Tate $R$ -motivic spectra

The trace of the local $A^{1}$ -degree