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arXiv · 2408.13910

A non-abelian version of Deligne's Fixed Part Theorem

Hélène Esnault·Moritz Kerz
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Abstract

We formulate and prove a non-abelian analog of Deligne's Fixed Part theorem on Hodge classes, revisiting previous work of Jost--Zuo, Katzarkov--Pantev and Landesman--Litt. To this aim we study algebraically isomonodromic extensions of local systems and we relate them to variations of Hodge structures, for example we show that the Mumford-Tate group at a generic point stays constant in an algebraically isomonodromic extension of a variation of Hodge structure. v2: a few typos ironed and Thm 1.1 5) completed. v3: there was a Schlamassel leading to a mix-up of files. Apologies. Else identical version (one minor change). v5 final version. Appears in Alg. Geom.

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Hélène Esnault, Moritz Kerz. 2024-08-25. A non-abelian version of Deligne's Fixed Part Theorem. https://arxiv.org/abs/2408.13910

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