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

作　　者：Yun Feng JIANG 

机构地区：[1]Department of Mathematics,University of Kansas,405 Snow Hall,1460 Jayhawk Blvd,Lawrence USA

出　　处：《Acta Mathematica Sinica,English Series》2022年第10期1722-1780,共59页数学学报（英文版）

基　　金：Partially supported by NSF(Grant No.DMS-1600997)。

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

关 键 词：Non-archimedean Donaldson-Thomas theory Berkovich space analytic d-critical scheme motivic localization 

分 类 号：O177[理学—数学]