arXiv subjects

Ivan Tomašić

Publications and source records attributed to Ivan Tomašić.

5 recordsLinked to original sources

arXiv2025

Galois theory of differential schemes

Since 1883, Picard-Vessiot theory had been developed as the Galois theory of differential field extensions associated to linear differential equations. Inspired by categorical Galois theory of Janelidze, and by using novel methods of precategorical descent applied to algebraic-geometric situations, we develop a Galois theory that applies to morphisms of differential schemes, and vastly generalises the linear Picard-Vessiot theory, as well as the strongly normal theory of Kolchin.

math.AG↗

arXiv2022

Graphons arising from graphs definable over finite fields

We prove a version of Tao's algebraic regularity lemma for asymptotic classes in the context of graphons. We apply it to study expander difference polynomials over fields with powers of Frobenius.

math.LO↗

arXiv2018

Strongly étale difference algebras and Babbitt's decomposition

We introduce a class of strongly étale difference algebras, whose role in the study of difference equations is analogous to the role of étale algebras in the study of algebraic equations. We deduce an improved version of Babbitt's decomposition theorem and we present applications to difference algebraic groups and the compatibility problem.

math.AG↗

arXiv2017

Direct twisted Galois stratification

The theory ACFA admits a primitive recursive quantifier elimination procedure. It is therefore primitive recursively decidable.

math.LO↗

arXiv2012

A twisted theorem of Chebotarev

We prove a function-field version of Chebotarev's density theorem in the framework of difference algebraic geometry by developing the notion of Galois coverings of generalised difference schemes, and using Hrushovski's twisted Lang-Weil estimate.

math.AG↗