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arXiv · 2407.01379

Tannakian fundamental groups of blended extensions

Payman Eskandari
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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.

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Payman Eskandari. 2026-08-05. Tannakian fundamental groups of blended extensions. https://arxiv.org/abs/2407.01379

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