Ishan Levy

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20212024

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K

-theoretic counterexamples to Ravenel's telescope conjecture

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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.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.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…

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

Categorifying reduced rings

On the K-theory of regular coconnective rings

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