Abstract

We define a $p$-adic étale Tate twist for a modulus pair $(X,D)$, where $X$ is a regular semistable family and $D$ is an effective Cartier divisor on $X$ that is flat over a base scheme. Our main result is an arithmetic duality of $p$-adic étale Tate twists for proper modulus pairs $(X,D)$, which holds as a pro-system with respect to the multiplicities of the irreducible components of $D$.

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