Alapan Mukhopadhyay

activity

20162026

most citedHigh Frobenius pushforwards generate the bounded derived category

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

collaborators

8 papers

math.AC2026

A dynamical approach to Frobenius splitting

Alapan Mukhopadhyay, Ilya Smirnov

A dynamical system can be associated to the process of decomposing iterated Frobenius pushforwards of modules into indecomposable direct summands. Via this connection, we apply the…

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

Alapan Mukhopadhyay, Karen E. Smith

We prove that under suitable graded and local hypothesis, a formally unramified algebra over a field must be reduced. We detail examples, including one due to Gabber, to show that…

math.AG2016

Multi-point Seshadri constants on ruled surfaces

Krishna Hanumanthu, Alapan Mukhopadhyay

Let $X$ be a surface and let $L$ be an ample line bundle on $X$ . We first obtain a lower bound for the Seshadri constant $ε (X, L, r)$ , when $r \geq 3$ . We then assume that $…