On Galois realizations of special linear groups

TL;DR

This paper explores methods to realize special linear groups as Galois groups over the rationals by analyzing determinants of specific etale sheaves constructed through middle convolution.

Contribution

It introduces a novel approach using middle convolution to construct Galois realizations of special linear groups over the rationals.

Findings

Successful construction of Galois realizations for certain special linear groups.

New techniques for analyzing determinants of etale sheaves.

Advancement in inverse Galois problem methods.

Abstract

We study the determinant of certain etale sheaves constructed via middle convolution in order to realize special linear groups regularly as Galois groups over the rationals.