On the universal extensions in Tannakian categories

Abstract

We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness of some homotopy sequences for these categories and to study $F$-able isocrystals.

arXiv comment19 pages; added reference to [And20]

References in corpus (4)

• On Nori's Fundamental Group Scheme
• The monodromy groups of lisse sheaves and overconvergent $F$-isocrystals
• Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties
• Local acyclicity in $p$-adic cohomology

Cited by in corpus (3)

• Maximal tori of monodromy groups of $F$-isocrystals and an application to abelian varieties
• Malcev Completions, Hodge Theory, and Motives
• Slopes of $F$-isocrystals over abelian varieties