Casimir Kothari

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math.AG2024

Duality of differential operators and algebraic de Rham cohomology

Caleb Ji, Casimir Kothari, Oliver Li +3

Given a smooth proper morphism $f : X \to S$ , we introduce a certain derived category where morphisms are permitted to be $O_{S}$ -linear differential operators.…

math.AG2024

Dieudonné theory for $n$ -smooth group schemes

Casimir Kothari, Joshua Mundinger

For all $n \geq 1$ , there is a notion of an $n$ -smooth group scheme over any $F_{p}$ -algebra $R$ , which may be thought of as a ``Frobenius analogue" of an $n$ -truncated Bars…

math.AG2023

Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$

Casimir Kothari

We construct smooth projective families of algebraic varieties in characteristic $p$ such that the dimensions of the de Rham and Hodge cohomology groups of the fibers can be made t…

Duality of differential operators and algebraic de Rham cohomology

Dieudonné theory for n-smooth group schemes

Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic p

Dieudonné theory for $n$ -smooth group schemes

Arbitrarily large jumps in the de Rham and Hodge cohomology of families in characteristic $p$