Monodromy of local systems and applications to coding theory

Abstract

The present work concerns the study of monodromy of ℓ-adic sheaves with an strong focus on computational matters. After reviewing ´etale and ℓ-adic cohomology, we introduce some families of local systems and consider the problem of determining whether their monodromy is finite or not. To this end, we propose a sieve-based approach and an algorithm is described. Actual implementations are used to explore the question for the described families and to compare the outputs with recent results in the area. The algorithm is further used to obtain some numerical data showing certain phenomena that allows us to identify major obstructions to the performance of the implementations. We conclude with some motivation coming from coding theory and cryptography as well as an application of the study of monodromy to coding theory.