Algebraic flat connections and o-minimality

Abstract

We prove that an algebraic flat connection has definable flat sections in the analytic exponential structure if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker and Mullane. This provides an o minimal characterisation of classical properties of the Gauss-Manin connection. v2: a few typos removed. Appears in the Laumon Volume, Springer Verlag, Simons subseries.

9 pages