Duality for p-adic \'etale Tate Twists with modulus

TL;DR

This paper develops a duality theory for p-adic étale Tate twists associated with modulus pairs, extending the understanding of their arithmetic properties in the context of semi-stable families and Cartier divisors.

Contribution

It introduces a new framework for p-adic étale Tate twists with modulus and establishes an arithmetic duality theorem for proper modulus pairs.

Findings

Established an arithmetic duality for p-adic étale Tate twists

Extended duality to pro-systems with respect to divisor multiplicities

Provided a new perspective on the arithmetic of semi-stable families

Abstract

In this paper, we define p-adic \'etale Tate twists for a modulus pair (X,D), where X is a regular semi-stable family and D is an effective Cartier divisor on X which is flat over a base scheme. The main result of this paper is an arithmetic duality of p-adic \'etale 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.