In this paper, we define a syntomic complex for modulus pair $(X,D)$, where $X$ is a regular semi-stable family and $D$ is an effective Cartier divisor on $X$ and we compute its cohomology sheaves. We construct a symbol map for this syntomic complex for modulus pair $(X,D)$ and investigate its cokernel by computing its cohomology sheaves. To compute the structure of the cohomology sheaves of syntomic complex with modulus, we define some filtrations on it.
"On Syntomic Complexes with Modulus for Semi-stable Reduction Cases." Tokyo J. Math. 44 (1) 175 - 233, June 2021. https://doi.org/10.3836/tjm/1502179342