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arXiv · 1807.09983

Wildly Ramified Rigid $G_2$-Local Systems

Konstantin Jakob
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Abstract

In earlier work of the author rigid irregular connections with differential Galois group $G_2$ and whose slopes have numerator $1$ were classified and new rigid connections were constructed. The same construction can be carried out for $\ell$-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 $G_2$-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.

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Konstantin Jakob. 2018-07-26. Wildly Ramified Rigid $G_2$-Local Systems. https://doi.org/10.1112/blms.12881

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