Periodic de Rham bundles over curves

Abstract

In this article, we introduce the notion of periodic de Rham bundles over smooth complex curves. We prove that motivic de Rham bundles over smooth complex curves are periodic. We conjecture that irreducible periodic de Rham bundles over smooth complex curves are motivic. We show that the conjecture holds for rank one objects and rigid objects.

42 pages. This is the second version. Comments are very welcome!

References in corpus (3)

• Logarithmic nonabelian Hodge theory in characteristic p
• Periodic Higgs subbundles in positive and mixed characteristic
• Characterization of Beauville's algebraic numbers via Hodge theory

Cited by in corpus (1)

• Tensor product theorem for parabolic $\lambda$-connections