On standard models of conic fibrations over a field of characteristic zero

TL;DR

This paper extends Sarkisov's 1982 result by proving the existence of standard models for three-dimensional conic fibrations over any characteristic zero field with finite group actions.

Contribution

It generalizes the existence of standard models of conic fibrations to arbitrary fields of characteristic zero with finite group actions.

Findings

Established the existence of standard models for three-dimensional conic fibrations over arbitrary characteristic zero fields.

Extended Sarkisov's 1982 results to include fields with finite group actions.

Provided foundational results for the classification of conic fibrations in broader algebraic settings.

Abstract

In 1982 V.G. Sarkisov proved the existense of standard models of conic fibrations over algebraically closed fields of $\operatorname{char}\neq 2$. In this paper we will prove the analogous result for three-dimensional conic fibrations over arbitrary fields of characteristic zero with a finite group action.