Wildly ramified rigid G2$G_2$‐local systems

Abstract

AbstractIn earlier work of the author, rigid irregular connections with differential Galois group and whose slopes have numerator 1 were classified and new rigid connections were constructed. The same construction can be carried out for ‐adic local systems in the setting of positive characteristic. In this article, we provide the results that are needed to obtain the classification of wildly ramified rigid ‐local systems whose slopes have numerator 1. The overall strategy of the classification is very similar but the methods needed to obtain some invariants differ.