Tannakian duality over Dedekind rings and applications

Abstract

We establish a duality between flat affine group schemes and rigid tensor categories equipped with a neutral fiber functor (called Tannakian lattice), both defined over a Dedekind ring. We use this duality and the known Tannakian duality due to Saavedra to study morphisms between flat affine group schemes. Next, we apply our new duality to the category of stratified sheaves on a smooth scheme over a Dedekind ring R to define the relative differential fundamental group scheme of the given scheme and compare the fibers of this group scheme with the fundamental group scheme of the fibers. When R is a complete DVR of equal characteristic we show that this category is Tannakian in the sense of Saavedra.

41 pages, final version, accepted for publication in Mathematische Zeitschrift

References in corpus (1)

• On an injectivity lemma in the proof of Tannakian duality

Cited by in corpus (7)

• Sur l'existence du schéma en groupes fondamental
• Regular-singular connections on relative complex schemes
• The geometric Satake equivalence for integral motives
• Prolongation of regular singular connections on punctured affine line over a Henselian ring
• On the structure of affine flat group schemes over discrete valuation rings, II
• On the flatness and the projectivity over Hopf subalgebras of Hopf algebras over discrete valuation rings
• Extension of torsors and prime to $p$ fundamental group scheme