# The Noether problem for spinor groups of small rank

## TL;DR

This paper proves that the Noether Problem has a positive solution for spinor groups of rank up to 14 over any field with characteristic not equal to 2, extending previous results in the area.

## Contribution

It extends the known cases where the Noether Problem is positively resolved for spinor groups up to rank 14, building on prior foundational work.

## Key findings

- Positive solution for $ ext{Spin}_n$ with $n extless 15$ over arbitrary fields of characteristic not 2
- Generalizes previous results to higher ranks
- Provides new insights into the structure of spinor groups and their invariants

## Abstract

Building on prior work of Bogomolov, Garibaldi, Guralnick, Igusa, Kordonskii, Merkurjev and others, we show that the Noether Problem for $\operatorname{Spin}_n$ has a positive solution for every $n\leq 14$ over an arbitrary field of characteristic $\neq 2$.