Non-abelian Hodge theory for non-proper varieties and the linear Shafarevich conjecture

Published 24 Mar 2026 in math.AG | (2603.23467v1)

Abstract: We survey recent advances in non-abelian Hodge theory in the "mixed" setting of non-proper algebraic varieties. We then describe how these tools are used to construct algebraic Shafarevich morphisms and prove a version of the linear Shafarevich conjecture for any algebraic variety.

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Benjamin Bakker

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