Allen Yuan

activity

20142023

most citedThe Chromatic Nullstellensatz

6 citations · 24 across the 12 of their papers we have counts for

collaborators

13 papers

math.RT2023

$G$ -spectra of cyclic defect

Tony Feng, David Treumann, Allen Yuan

Broué's Abelian Defect Conjecture predicts interesting derived equivalences between derived categories of modular representations of finite groups. We investigate a generalization…

math.AT2022

The sphere of semiadditive height 1

Allen Yuan

We construct a lift of the $p$ -complete sphere to the universal height $1$ higher semiadditive stable $\infty$ -category tsade- $1$ of Carmeli--Schlank--Yanovski, providing a counter…

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.KT2021

Examples of chromatic redshift in algebraic $K$ -theory

Allen Yuan

We give a simple argument to detect chromatic redshift in the algebraic $K$ -theory of $E_{\infty}$ -ring spectra and give two applications: we show for $n \geq 1$ that $K(E_…

math.KT2021

Chromatic convergence for the algebraic K-theory of the sphere spectrum

Andrew J. Blumberg, Michael A. Mandell, Allen Yuan

We show that the map from $K (S)$ to its chromatic completion is a connective cover and identify the fiber in $K$ -theoretic terms. We combine this with recent work of Land…

math.AT2021★ 3 cited

Higher semiadditive Grothendieck-Witt theory and the $K (1)$ -local sphere

Shachar Carmeli, Allen Yuan

We develop a higher semiadditive version of Grothendieck-Witt theory. We then apply the theory in the case of a finite field to study the higher semiadditive structure of the $K(1)…

math.KT2021★ 1 cited

A version of Waldhausen's chromatic convergence for $T C$

Andrew J. Blumberg, Michael A. Mandell, Allen Yuan

The map $T C (S)_{p}^{\land} \to holim T C (L_{n} S)_{p}^{\land}$ is a weak equivalence.

math.AT2019

Wilson Spaces, Snaith Constructions, and Elliptic Orientations

Hood Chatham, Jeremy Hahn, Allen Yuan

We construct a canonical family of even periodic $E_{\infty}$ -ring spectra, with exactly one member of the family for every prime $p$ and chromatic height $n$ . At height $…

math.AT2019★ 3 cited

Integral Models for Spaces via the Higher Frobenius

Allen Yuan

We give a fully faithful integral model for spaces in terms of $E_{\infty}$ -ring spectra and the Nikolaus-Scholze Frobenius. The key technical input is the development of…

math.AT2019★ 5 cited

Exotic Multiplications on Periodic Complex Bordism

Jeremy Hahn, Allen Yuan

Victor Snaith gave a construction of periodic complex bordism by inverting the Bott element in the suspension spectrum of $B U$ . This presents an $E_{\infty}$ structure on pe…

math.AT2017★ 4 cited

Multiplicative Structure in the Stable Splitting of $Ω S L_{n} (C)$

Jeremy Hahn, Allen Yuan

The space of based loops in $S L_{n} (C)$ , also known as the affine Grassmannian of $S L_{n} (C)$ , admits an $E_{2}$ or fusion product. Work of Mitchell and Richte…

math.AG2014

Irreducible Canonical Representations in Positive Characteristic

Benjamin Gunby, Alexander Smith, Allen Yuan

For $X$ a curve over a field of positive characteristic, we investigate when the canonical representation of $Aut (X)$ on $H^{0} (X, Ω_{X})$ is irreducible. Any curve with an irre…

math.NT2014★ 2 cited

Proof of a conjecture of Guy on class numbers

Lynn Chua, Benjamin Gunby, Soohyun Park +1

It is well known that for any prime $p \equiv 3$ (mod $4$ ), the class numbers of the quadratic fields $Q (p)$ and $Q (- p)$ , $h (p)$ and $h (- p)$ respecti…

G-spectra of cyclic defect

The sphere of semiadditive height 1

The Chromatic Nullstellensatz

Examples of chromatic redshift in algebraic K-theory

Chromatic convergence for the algebraic K-theory of the sphere spectrum

Higher semiadditive Grothendieck-Witt theory and the K(1)-local sphere

A version of Waldhausen's chromatic convergence for TC

Wilson Spaces, Snaith Constructions, and Elliptic Orientations

Integral Models for Spaces via the Higher Frobenius

Exotic Multiplications on Periodic Complex Bordism

Multiplicative Structure in the Stable Splitting of ΩSLn​(C)

Irreducible Canonical Representations in Positive Characteristic

Proof of a conjecture of Guy on class numbers

$G$ -spectra of cyclic defect

Examples of chromatic redshift in algebraic $K$ -theory

Higher semiadditive Grothendieck-Witt theory and the $K (1)$ -local sphere

A version of Waldhausen's chromatic convergence for $T C$

Multiplicative Structure in the Stable Splitting of $Ω S L_{n} (C)$