Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Introduction to lie algebras and representation theory

In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the following two cases: (1) the complexes of sheaves of $\mathcal O$-modules on the \v{C}ech nerve of an open cover of a ringed space $(X, \mathcal O)$; (2) the complexes of sheaves on the simplicial nerve of a discrete group $G$ acting on a space. The explicit models we obtain in this way are twisted complexes as well as their $D$-module and $G$-equivariant versions. As an application we show that there is a stack of twisted perfect complexes.

https://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2017/0019/0002/HHA-2017-0019-0002-a017.pdf

Explicit homotopy limits of dg-categories and twisted complexes

Operator Theory/Operator Algebras and Applications, Part 1

/pdf/on-discrete-series-biao-xian-lun-toda-yu-jie-xi-xue-5bi34fgxci.pdf

On Discrete Series (表現論と大域解析学)

We study the dg-category of twisted complexes on a ringed space and prove that it gives a new dg-enhancement of the derived category of perfect complexes on that space. A twisted complex is a collection of locally defined sheaves together with the homotopic gluing data. We construct a dg-functor from twisted complexes to perfect complexes, which turns out to be a dg-enhancement. This new enhancement has the advantage of being completely geometric and it comes directly from the definition of perfect complex. In addition we will talk about some applications and further topics around twisted complexes.

/pdf/twisted-complexes-on-a-ringed-space-as-a-dg-enhancement-of-4l06vjeb7a.pdf

Twisted complexes on a ringed space as a dg-enhancement of the derived category of perfect complexes

In this paper we study the homotopy limits of cosimplicial diagrams of dg-categories. We first give an explicit construction of the totalization of such a diagram and then show that the totalization agrees with the homotopy limit in the following two cases: (1) the complexes of sheaves of $\mathcal O$-modules on the Cech nerve of an open cover of a ringed space $(X, \mathcal O)$; (2) the complexes of sheaves on the simplicial nerve of a discrete group $G$ acting on a space. The explicit models we obtain in this way are twisted complexes as well as their $D$-module and $G$-equivariant versions. As an application we show that there is a stack of twisted perfect complexes.

Given a compact complex manifold, the purpose of this paper is to construct the Chern character for coherent sheaves with values in Bott-Chern cohomology, and to prove a corresponding Riemann-Roch-Grothendieck formula. Our paper is based on a fundamental construction of Block.

Coherent sheaves, superconnections, and RRG

BAUM-CONNES CONJECTURE, FLAG VARIETIES AND REPRESENTATIONS OF SEMISIMPLE LIE GROUPS Zhaoting Wei Jonathan Block This thesis consists of three chapters. In Chapter 1 we review the Baum-Connes conjecture and its relation with representation theory In Chapter 2 we describe the equivariant K-theory of the real semisimple Lie group which acts on the (complex) ag variety of its complexi cation group. We construct an assembly map in the framework of KK-theory. Then we prove that it is an isomorphism. The prove relies on a careful study of the orbits of the real group action on the ag variety and then piecing together the orbits. This result can be considered as a special case of the Baum-Connes conjecture with coe cient. In Chapter 3 we study the noncommutative Poisson bracket P on the classical family algebra Cτ (g). We show that P is the rst-order deformation from Cτ (g) to Qτ (g) where the later is the quantum family algebra. We will prove that the noncommutative Poisson bracket is in fact a Hochschild 2-coboundary therefore the deformation is in nitesimally trivial. In the appendix we talk about some further topics and open problems in this area.

Baum-Connes conjecture, flag varieties and representations of semisimple Lie groups

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Papers

Explicit homotopy limits of dg-categories and twisted complexes

Twisted complexes on a ringed space as a dg-enhancement of the derived category of perfect complexes

Explicit homotopy limits of dg-categories and twisted complexes

Coherent sheaves, superconnections, and RRG

Baum-Connes conjecture, flag varieties and representations of semisimple Lie groups