Goursat rigid local systems of rank four
Abstract
We study the general properties of certain rank four rigid local systems considered by Goursat. We analyze when they are irreducible, give an explicit integral description as well as the invariant Hermitian form when it exists. By a computer search we find what we expect are all irreducible such systems all whose solutions are algebraic functions and give several explicit examples defined over the rationals. We also exhibit one example with infinite monodromy as arising from a family of genus two curves.
 Publication:

arXiv eprints
 Pub Date:
 March 2018
 DOI:
 10.48550/arXiv.1803.08379
 arXiv:
 arXiv:1803.08379
 Bibcode:
 2018arXiv180308379R
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Algebraic Geometry