Duality for p-adic étale Tate Twists with modulus

Abstract

In this paper, we define p-adic étale 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 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. m 21 5.1. Setting 22 5.2. Construction of Θ r D 22 5.3. Explicit formula for Θ r D 23 5.4. Proof of (⊛2) 28 6. Duality for M r m 28 6.1. Proof of Theorem 6.1 30 7. Proof of Theorem 1.1 33 8. Proof of non-degeneracy of the pairing in Theorem 1.1 37 8.1. Descending induction on r 37 8.2. Proof of Proposition 39 9. Acknowledgements 42 References 42