# On Galois descent of complete intersections

## TL;DR

This paper introduces a new concept of strict complete intersections related to Cox rings and proves that this property descends through Galois extensions, advancing the understanding of algebraic structures under field extensions.

## Contribution

It defines strict complete intersections in the context of Cox rings and establishes Galois descent for this class, a novel theoretical development.

## Key findings

- Galois descent holds for strict complete intersections in Cox rings
- New notion of strict complete intersections introduced
- Advances understanding of algebraic structures under Galois actions

## Abstract

We introduce a notion of strict complete intersections with respect to Cox rings and we prove Galois descent for this new notion.