Silting Reduction in Exact Categories

Presilting and silting subcategories in extriangulated categories were introduced by Adachi and Tsukamoto recently, which are generalizations of those concepts in triangulated categories. Exact categories and triangulated categories are extriangulated categories. In this paper, we prove that the Gabriel-Zisman localization ℬ/(𝒲) of an exact category ℬ with respect to a presilting subcategory 𝒲 satisfying certain condition can be realized as a subfactor category of ℬ . Afterwards, we discuss the relation between silting subcategories and tilting subcategories in exact categories, which gives us a kind of important examples of our results. In particular, for a finite dimensional Gorenstein algebra, we get the relative version of the description of the singularity category due to Happel and Chen-Zhang.