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令R是左Gorenstein环.我们构造了奇点反导出模型范畴和奇点余导出模型范畴(见文[Models for singularity categories,Adv Math.,2014,254:187-232])之间的Quillen等价.作为应用,给出了投射,内射模的正合复形的同伦范畴之间的一个具体的等价■. 相似文献
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设C 是加法范畴, 态射φ,η: X→ X 是C上的态射. 若φ,η 具有Drazin逆且φη =0, 则φ+η 也具有Drazin逆. 若φ具有Drazin逆φD 且1X+φDη 可逆, 作者讨论f =φ+η 的Drazin逆( 群逆)并且给出 f D(f #}=(1X+φDη)-1φD的充分必要条件. 最后, 把Huylebrouck的结果从群逆推广到了Drazin逆. 相似文献
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文章研究了三角范畴D及其coherent函子范畴A(D)的recollement之间的关系.利用D的recollement可以诱导A(D)的prerecollement,文章证明了该prerecollement是recollement的充分必要条件是D的recollement是可裂的;并且D的recollement可以诱导A(D)的prerecollement. 相似文献
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本文首先在一般的赋范线性空间中研究了集值映射F;X→Y的平衡点的存在性问题,证明了包含问题O∈F(X)的三个可解性定理.然后在无穷维空间中研究了弱相依锥Tkσ(x)的直接像,弱相依导数DσF(x,y)的一个链式法则以及偏y弱导数DyσF(x,y)的弱Lip连续性.最后,作为应用,给出并证明了用弱相依导数DσF(x,y)及弱P导数PσF(x,y)判定无穷维 相似文献
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考虑Hnon映射Ta.b,对于正测度的参数集合,构造了Ta.b的拓扑可迁的奇怪吸引子Λa.b的一个捕捉区G,证明Λa.b=Ta.bnG,同时证明Λa.b的吸引域恰好就是那些边界包含在Wu(P)∪Ws(P)中的区域的并以及Ws(P),从而肯定地回答了Benedicks和Carleson关于奇怪吸引子的吸引域的猜测。 相似文献
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设 μ 是 [0, 1)上的正规函数,Bn 是 n 维复空间 Cn 上的单位球, ψ 是 Bn 上的一个全纯函数,? 是 Bn 上的全纯自映射. 作者考虑如下一种积分算子:T?,ψ(f)(z) =Z01f[?(tz)]Rψ(tz)dt/t, z ∈ Bn.作者主要刻画了正规权Dirichlet型空间Dpμ(Bnn) (0 < p ≤ 1) 上 T?,ψ 的有界性和紧性.同时, 本文利用Carleson 方块和Bergman球的测度讨论了正规权Bergman型空间Apμ(Bn) 到 Dpμ(Bn) (p > 0)的同样问题. 对讨论的情形本文均给出了充要条件. 相似文献
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在[4]中我们对空间LR+q、1≤q≤2,讨论了函数的逻辑导数与积分。例如,建立了下列公式D(1)(I(1)f)=f,I(1)(D(1)f)=f. 但那里的方法不能用于q>2情形。本文是[4]的继续.对2
R+q的Walsh-Fourie 相似文献
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We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov–Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective model structure and also a projective model structure in case the category has enough projectives. As examples we show that if X is a locally Gorenstein projective scheme then the category ??????(X) of quasi‐coherent sheaves on X is such a category and so has these features. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Ren W.Zhang C.X. 《数学学报》2022,(5):849-858
In general, the properties of modules over a triangular matrix ring T = (0ABU) are studied via modules over diagonal “small rings” A and B. However, we use model structures on the category of T-modules to characterize the stable categories GP(A), GP(B) of Gorenstein projective modules over A and B. To this end, we introduce two subcategories of Gorenstein T-modules, and obtain two corresponding complete cotorsion pairs. Moreover, cotorsion pairs of modules are lifted to T-complexes, and the equivalences and recollements of homotopy categories of complexes are studied. © 2022 Chinese Academy of Sciences. All rights reserved. 相似文献
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Let R be a right coherent ring and D~b(R-Mod) the bounded derived category of left R-modules. Denote by D~b(R-Mod)_([G F,C]) the subcategory of D~b(R-Mod) consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K~b(F ∩ C) the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D~b(R-Mod)_([G F,C])/K~b(F ∩ C) is triangle-equivalent to the stable category GF ∩ C of the Frobenius category of all Gorenstein flat and cotorsion left R-modules. 相似文献
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本文证明了任意环的整体Ding投射维数和整体Ding内射维数一致,研究了奇点范畴和相对于Ding模的稳定范畴间的关系,并刻画了Gorenstein (正则)环以及环的整体维数的有限性. 相似文献
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In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜C(R) and that in the Bass class ?C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories. 相似文献
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We study groups whose cohomology functors commute with filtered colimits in high dimensions. We relate this condition to the existence of projective resolutions which exhibit some finiteness properties in high dimensions, and to the existence of Eilenberg–Mac Lane spaces with finitely many n-cells for all sufficiently large n. To that end, we determine the structure of completely finitary Gorenstein projective modules over group rings. The methods are inspired by representation theory and make use of the stable module category, in which morphisms are defined through complete cohomology. In order to carry out these methods, we need to restrict ourselves to certain classes of hierarchically decomposable groups. 相似文献
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We define a notion of total acyclicity for complexes of flat quasi-coherent sheaves on a semi-separated noetherian scheme, and study these complexes using the pure derived category of flat quasi-coherent sheaves. We prove that a scheme is Gorenstein if and only if every acyclic complex of flat quasi-coherent sheaves is totally acyclic. Our formalism also removes the need for a dualising complex in several known results for rings, including Jørgensen's proof of the existence of Gorenstein projective precovers. 相似文献