The Moduli Space of Stable Coherent Sheaves via Non-archimedean Geometry

We provide a construction of the moduli space stable coherent sheaves in world non-archimedean geometry, where we use notion Berkovich analytic spaces. The motivation for our is Tony Yue Yu’s enumerative geometry Gromov—Witten theory. using spaces will give rise to version Donaldson—Thomas invariants. In this paper over field $${\mathbb{K}}$$ . machinery formal schemes, that is, define and construct stack (semi)-stable discrete valuation ring R, taking generic fiber get semistable fractional generalize Joyce’s d-critical scheme structure [37] or Kiem—Li’s virtual critical manifolds [38] As an application, proof motivic localization formula -analytic global motive vanishing cycles integration on oriented schemes. This generalizes Maulik’s