On irreducibility of six-dimensional compatible systems of $\mathbb{Q}$

Boyi Dai

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arXiv · 2503.04541

On irreducibility of six-dimensional compatible systems of $\mathbb{Q}$

Boyi Dai

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Abstract

We study the irreducibility of 6-dimensional strictly compatible systems of Q with distinct Hodge-Tate weights. We prove that if one of the representations $\rho$ in such a system is irreducible and satisfies a self-dual condition $\rho^{\vee}\otimes\chi\cong\rho$ for some character $\chi$, then all but finitely many of them are irreducible.

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Boyi Dai. 2025-03-06. On irreducibility of six-dimensional compatible systems of $\mathbb{Q}$. https://arxiv.org/abs/2503.04541

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