Casimir Kothari

activity

20192026

collaborators

5 papers

math.AG2026

Cartier--Dieudonné Theory of Connected Group Schemes

Casimir Kothari, Joshua Mundinger

We prove that fiberwise-connected finite locally free commutative group schemes over a ring $R$ are equivalent to an explicit full subcategory of the derived category of modules ov…

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…

math.NT2019

The Explicit Sato-Tate Conjecture For Primes In Arithmetic Progressions

Trajan Hammonds, Casimir Kothari, Noah Luntzlara +3

Let $τ (n)$ be Ramanujan's tau function, defined by the discriminant modular form \[ Δ(z) = q\prod_{j=1}^{\infty}(1-q^{j})^{24}\ =\ \sum_{n=1}^{\infty}τ(n) q^n \,,q=e^{2πi z} \] (th…