Tannakian fundamental groups of blended extensions

Abstract

Let $A_1,A_2,A_3$ be objects in a neutral tannakian category over a field of characteristic zero. Let $L$ be an extension of $A_2$ by $A_1$, and $N$ an extension of $A_3$ by $A_2$. Let $M$ be a blended extension (extension panachée) of $N$ by $L$. We study the subgroup of the tannakian fundamental group of M that acts trivially on $A_1,A_2$, and $A_3$. We also give an application to the unipotent part of the motivic version of the Hodge conjecture (i.e., the equality of the unipotent radicals of the motivic Galois and Mumford-Tate groups) for Deligne 1-motives.

arXiv commentFinal version: Minor changes made based on referee comments