# On syntomic complex with modulus for semi-stable reduction case

## TL;DR

This paper introduces a syntomic complex for modulus pairs involving semi-stable families and computes its cohomology sheaves, advancing the understanding of p-adic cohomology in algebraic geometry.

## Contribution

It defines a new syntomic complex for modulus pairs with semi-stable reduction and calculates its cohomology sheaves, extending existing theories.

## Key findings

- Cohomology sheaves of the syntomic complex are explicitly computed.
- The syntomic complex is defined for semi-stable families with divisors.
- The work advances p-adic cohomology theories for algebraic varieties.

## Abstract

In this paper, we define syntomic complex for modulus pair (X,D), where X is regular semi-stable family and D is an effective Cartier divisor on X. We compute its cohomology sheaves.