2024/08/25 by Esnault, Hélène, Kerz, Moritz
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2408.13910
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). v4 Appendix A reshaped.