  We study the middle convolution of local systems on the punctured affine line
in the setting of singular cohomology and in the setting of \'etale cohomology.
We derive a formula to compute the topological monodromy of the middle
convolution in the general case and use it to deduce some irreducibility
criteria. Then we give a geometric interpretation of the middle convolution in
the \'etale setting.
  This geometric approach to the convolution and the theory of Hecke characters
yields information on the occurring arithmetic determinants. We employ these
methods to realize special linear groups regularly as Galois groups over ${\bf
Q}(t).$

Number Theory;Algebraic Geometry