arXiv subjects

Ioannis Tsouknidas

Publications and source records attributed to Ioannis Tsouknidas.

5 recordsLinked to original sources

arXiv2025

On the Hasse-Arf property of local fields

Let $F/K$ be a finite Galois totally & wildly ramified extension of complete discrete valuation fields. We say that the extension has the Hasse-Arf property if the ramification jumps in upper numbering are integers. We give necessary defining equations for $F$ in terms of the ramification jumps. In order for the Hasse-Arf property to hold, these equations become very strict. We prove that the last assertion is an equivalence condition, thus in terms of these defining equations, the Hasse-Arf property becomes an equivalence condition.

math.NT↗

arXiv2023

A generalization of the Hasse-Arf theorem

We use the theory of Harbater-Katz-Gabber curves to derive a generalization of the Hasse-Arf theorem for complete local field extensions in positive characteristic.

math.AG↗

arXiv2020

A generating set for the canonical ideal of HKG-curves

The canonical ideal for Harbater Katz Gabber covers satisfying the conditions of Petri's theorem is studied and an explicit non-singular model of the above curves is given.

math.AG↗

arXiv2020

A cohomological treatise of HKG-covers with applications to the Nottingham group

We characterize Harbater-Katz-Gabber curves in terms of a family of cohomology classes satisfying a compatibility condition. Our construction is applied to the description of finite subgroups of the Nottingham Group.

math.AG↗

arXiv2019

Automorphisms and the canonical ideal

The automorphism group of a curve is studied from the viewpoint of the canonical embedding and Petri's theorem. A criterion for identifying the automorphism group as an algebraic subgroup the general linear group is given. Furthermore the action of the automorphism group is extended to an action of the minimal free resolution of the canonical ring of the curve $X$.

math.AG↗