Abstract
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.
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