Alapan Mukhopadhyay

activity

20162024

most citedHigh Frobenius pushforwards generate the bounded derived category

3 citations · 4 across the 7 of their papers we have counts for

collaborators

7 papers

math.AC2024

Some algebras with trivial rings of differential operators

Alapan Mukhopadhyay, Karen E. Smith

Let $k$ be an arbitrary field. We construct examples of regular local $k$ -algebras $R$ (of positive dimension) for which the ring of differential operators $D_{k} (R)$ is trivial in t…

math.AC2023

$h$ -function, Hilbert-Kunz density function and Frobenius-Poincaré function

Cheng Meng, Alapan Mukhopadhyay

Given ideals $I, J$ of a noetherian local ring $(R, m)$ such that $I + J$ is $m$ -primary and a finitely generated $R$ -module $M$ , we associate an invariant of $(M,…

math.AG2023★ 3 cited

High Frobenius pushforwards generate the bounded derived category

Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank +2

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme $X$ of prime characteristic. The main result is that when the Frobenius…

math.AG2022

Ind-étale vs Formally étale

Shubhodip Mondal, Alapan Mukhopadhyay

We show that when $A$ is a reduced algebra over a characteristic zero field $k$ and the module of Kähler differentials $Ω_{A / k} = 0$ , then $A$ is ind-étale, partially answering a que…

math.AC2022

Frobenius-Poincaré function and Hilbert-Kunz multiplicity

Alapan Mukhopadhyay

We generalize the notion of Hilbert-Kunz multiplicity of a graded triple $(M, R, I)$ in characteristic $p > 0$ by proving that for any complex number $y$ , the limit $$\underset{n \to \…

math.AC2020★ 1 cited

Reducedness of formally unramified algebras over fields