论文摘要
Grothendieck在上个世纪60年代初提出的概型理论,使代数几何进入一个全新的阶段。概型上的拟凝聚层和凝聚层分别起着环上的模和有限生成模的作用。因此自概型理论建立后,概型上的拟凝聚层和凝聚层一直是代数几何及相关学科的热门研究对象。本学位论文主要研究椭圆曲线上的拟凝聚层以及光滑曲线的凝聚层范畴的单扩张范畴。全文共分为五章。第一章介绍本学位论文的研究背景及有关方向的发展动态,并阐述本文的主要结论。第二章给出与本文密切相关的概念及其基本性质,为后面的章节提供必要的理论基础。第三章讨论椭圆曲线上的generic层。我们给出椭圆曲线上的generic层及generic层的rank,Euler特征,slope的定义,证明了generic层的slope属于Q∪{∞}。在此基础上,我们确定了所有的generic层:对于q∈Q∪{∞},在同构意义下存在唯一的slope为q的generic层Gq。特别地,有理函数层是slope为∞的generic层,而且任何一个generic层都可以通过拟凝聚层范畴的有界导出范畴上的一个正合自等价作用到有理函数层得到。我们进一步讨论了generic层与凝聚层的关系,证明可以利用generic层的垂范畴对凝聚层进行分类。第四章介绍椭圆曲线上generic层的构造。根据第三章中得到的有理函数层与generic层之间的关系,本章只讨论有理函数层的构造。我们首先给出椭圆曲线上无挠可除层的一种有效的构造方法,接着指出有理函数层在同构意义下是唯一的不可分解的无挠可除层,由此找到了有理函数层的一种构造方法。进一步,我们利用该方法来研究椭圆曲线上的有理函数层与凝聚层之间的关系,得到椭圆曲线上slope为∞的半稳定凝聚层构成的满子范畴可由有理函数层来确定。第五章研究光滑曲线上凝聚层范畴的单扩张范畴。我们给出了abelian范畴的单扩张范畴的定义。对于Hom-有限的abelian范畴的单扩张范畴,我们找到了一个对象是不可分解的一个必要条件,并证明这个单扩张范畴中的单对象只能有两种形式。进一步,我们研究代数闭域上光滑曲线的凝聚层范畴的单扩张范畴,给出了单扩张范畴中的所有不可分解对象的一种分类,进而通过分析不可分解对象之间的关系,刻画了这个单扩张范畴的整体结构。
论文目录
相关论文文献
- [1].Generic regular decompositions for generic zero-dimensional systems[J]. Science China(Information Sciences) 2014(09)
- [2].Slicing Java Generic Programs Using Generic System Dependence Graph[J]. Wuhan University Journal of Natural Sciences 2009(04)
- [3].An XML-based approach to represent generic bill of materials[J]. Journal of Harbin Institute of Technology 2009(03)
- [4].Model of generic project risk element transmission theory based on data mining[J]. Journal of Central South University of Technology 2008(01)
- [5].Presburger算数中的f-generic型（英文）[J]. 逻辑学研究 2019(03)
- [6].Existence of Canards under Non-generic Conditions[J]. Chinese Annals of Mathematics 2009(03)
- [7].Quantum state tomography for generic pure states[J]. Science China(Physics,Mechanics & Astronomy) 2018(11)
- [8].Field validation of generic wind park models using fault records[J]. Journal of Modern Power Systems and Clean Energy 2019(04)
- [9].One-dimensional continuous analytic potential solution to generic oxide-silicon-oxide system[J]. Chinese Physics B 2010(06)
- [10].FDA approves first generic Advair Diskus[J]. Journal of Chinese Pharmaceutical Sciences 2019(02)
- [11].A generic construction of low correlation zone sequences based on interleaved technique[J]. Science China(Mathematics) 2013(07)
- [12].Relative weak mixing is generic[J]. Science China(Mathematics) 2019(01)
- [13].基于DIgSILENT PowerFactory实现IEC第1类风电机组的标准建模(英文)[J]. 电力系统自动化 2013(08)
- [14].Improved particle filter based on fine resampling algorithm[J]. The Journal of China Universities of Posts and Telecommunications 2012(02)
- [15].ISO 31000的整合实施(英文)[J]. China Standardization 2013(06)
- [16].中国硕士论文引言之副标题的文类分析(英文)[J]. 当代外语研究 2013(10)
- [17].Extension of analytical indicial aerodynamics to generic trapezoidal wings in subsonic flow[J]. Chinese Journal of Aeronautics 2018(04)
- [18].A generic approach of integrating 3D models into virtual manufacturing[J]. Journal of Zhejiang University-Science C(Computers & Electronics) 2012(01)
- [19].Reducible Discord in Generic Three-Qubit Pure W States[J]. ZTE Communications 2013(03)
- [20].Semipositivity of generic ordinary fibration over a curve[J]. Science China(Mathematics) 2018(10)
- [21].GENERIC WARPED PRODUCT SUBMANIFOLDS OF LOCALLY CONFORMAL KEAHLER MANIFOLDS[J]. Acta Mathematica Scientia 2010(05)
- [22].Non-degeneracy of Extremal Points[J]. Chinese Annals of Mathematics(Series B) 2015(01)
- [23].Dynamics of different compound bursting in two phantom bursting mechanism models[J]. Science China(Technological Sciences) 2014(05)
- [24].InP photonic circuits using generic integration [Invited][J]. Photonics Research 2015(05)
- [25].Topological entropy of sets of generic points for actions of amenable groups[J]. Science China(Mathematics) 2018(05)
- [26].Experimental study of flow field distribution over a generic cranked double delta wing[J]. Chinese Journal of Aeronautics 2016(05)
- [27].APPLICATIONS OF NONLINEAR MEASURE ABOUT l~2-NORM TO SYNCHRONIZATION ANALYSIS OF COMPLEX NETWORKS VIA THE GENERAL INTERMITTENT CONTROL[J]. Annals of Applied Mathematics 2015(01)
- [28].Generic Regular Decompositions for Parametric Polynomial Systems[J]. Journal of Systems Science & Complexity 2015(05)
- [29].藥品專利鏈接:一個“雙贏”的制度設計[J]. 中国专利与商标 2018(01)
- [30].Linking the lab to the patient: Tools for optimizing oral drug delivery[J]. Asian Journal of Pharmaceutical Sciences 2016(01)