Ishan Levy

activity

20212024

most cited

K

-theoretic counterexamples to Ravenel's telescope conjecture

1 citations · 1 across the 9 of their papers we have counts for

collaborators

9 papers

math.KT2024

Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$ -theory

Jeremy Hahn, Ishan Levy, Andrew Senger

We prove for $n \geq c - 1$ that the functor taking an animated ring $R$ to its mod $(p^{c}, v_{1}^{p^{n}})$ syntomic cohomology factors through the functor $R \mapsto R / p^{c (n + 2)}$ , a pheno…

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

Topological Hochschild homology of the image of j

David Jongwon Lee, Ishan Levy

We compute the mod $(p, v_{1})$ and mod $(2, η, v_{1})$ $THH$ of many variants of the image-of- $J$ spectrum. In particular, we do this for $j_{ζ}$ , whose $TC$ is closely r…

math.KT2023

Categorifying reduced rings

Ishan Levy

Given a domain of characteristic zero $R$ , we functorially construct a rigid symmetric monoidal stable $\infty$ -category whose $K_{0}$ is $R$ , solving a problem of Khovanov. We also…

math.AT2022

The algebraic K-theory of the K(1)-local sphere via TC

Ishan Levy

We describe the algebraic K-theory of the $K (1)$ -local sphere and the category of type 2 finite spectra in terms of K-theory of discrete rings and topological cyclic homology. We f…

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.AT2021

The Borel Cohomology of Free Iterated Loop Spaces

Ishan Levy, Justin Wu

We compute the $SO (n + 1)$ -equivariant mod $2$ Borel cohomology of the free iterated loop space $Z^{S^{n}}$ when $Z$ is a mod $2$ generalized Eilenberg Mac Lane space. When $n = 1$ ,…

math.AT2021

Eilenberg Mac Lane spectra as p-cyclonic Thom spectra

Ishan Levy

Hopkins and Mahowald gave a simple description of the mod $p$ Eilenberg Mac Lane spectrum $F_{p}$ as the free $E_{2}$ -algebra with an equivalence of $p$ and $0$ . We s…

Crystallinity for syntomic cohomology, étale cohomology, and algebraic K-theory

K-theoretic counterexamples to Ravenel's telescope conjecture

Topological Hochschild homology of the image of j

Categorifying reduced rings

The algebraic K-theory of the K(1)-local sphere via TC

Adams-type maps are not stable under composition

On the K-theory of regular coconnective rings

The Borel Cohomology of Free Iterated Loop Spaces

Eilenberg Mac Lane spectra as p-cyclonic Thom spectra

Crystallinity for syntomic cohomology, étale cohomology, and algebraic $K$ -theory

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