典型文献
The Moduli Space of Stable Coherent Sheaves via Non-archimedean Geometry
文献摘要：
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 d-critical 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.
文献关键词：
中图分类号：
作者姓名：
Yun Feng JIANG
作者机构：
Department of Mathematics,University of Kansas,405 Snow Hall,1460 Jayhawk Blvd,Lawrence USA
文献出处：
引用格式：
[1]Yun Feng JIANG-.The Moduli Space of Stable Coherent Sheaves via Non-archimedean Geometry)[J].数学学报（英文版）,2022(10):1722-1780
A类：
Moduli,Sheaves,archimedean,Gromov,Donaldson,semistable,Kiem,motivic,Maulik
B类：
Space,Stable,Coherent,via,Non,Geometry,We,provide,construction,moduli,coherent,sheaves,world,geometry,where,we,use,notion,Berkovich,analytic,spaces,motivation,our,Tony,Yue,enumerative,Witten,theory,using,will,give,rise,version,Thomas,invariants,In,this,paper,over,field,machinery,formal,schemes,that,define,stack,discrete,valuation,ring,taking,generic,fiber,get,fractional,Joyce,critical,structure,Li,virtual,manifolds,application,proof,localization,formula,global,motive,vanishing,cycles,integration,oriented,This,generalizes
AB值：
0.372463
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