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

Commutative ring theory: Regular rings

Higher Algebraic K-Theory

Differential graded categories enhance our understanding of triangulated categories appearing in algebra and geometry. In this survey, we review their foundations and report on recent work by Drinfeld, Dugger-Shipley, ..., Toen and Toen-Vaquie.

On differential graded categories

We survey the basics of homological algebra in exact categories in the sense of Quillen All diagram lemmas are proved directly from the axioms, notably the five lemma, the 3 x 3-lemma and the snake lemma We briefly discuss exact functors, idempotent completion and weak idempotent completeness We then show that it is possible to construct the derived category of an exact category without any embedding into abelian categories and we sketch Deligne's approach to derived functors The construction of classical derived functors with values in an abelian category painlessly translates to exact categories, ie, we give proofs of the comparison theorem for projective resolutions and the horseshoe lemma After discussing some examples we elaborate on Thomason's proof of the Gabriel-Quillen embedding theorem in an appendix

Exact Categories

Idempotent completion of triangulated categories

We define negative K-groups for exact categories and for ``derived categories'' in the framework of Frobenius pairs, generalizing definitions of Bass, Karoubi, Carter, Pedersen-Weibel and Thomason. We prove localization and vanishing theorems for these groups. Devissage (for noetherian abelian categories), additivity, and resolution hold. We show that the first negative K-group of an abelian category vanishes, and that, in general, negative K-groups of a noetherian abelian category vanish. Our methods yield an explicit non-connective delooping of the K-theory of exact categories and chain complexes, generalizing constructions of Wagoner and Pedersen-Weibel. Extending a theorem of Auslander and Sherman, we discuss the K-theory homotopy fiber of e⊕→ e and its implications for negative K-groups. In the appendix, we replace Waldhausen's cylinder functor by a slightly weaker form of non-functorial factorization which is still sufficient to prove his approximation and fibration theorems.

https://rd.springer.com/content/pdf/10.1007%2Fs00209-005-0889-3.pdf

Negative K -theory of derived categories

https://homepages.warwick.ac.uk/~masiap/research/gwdg6.pdf

Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem

We study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian K-theory, of symmetric bilinear forms in exact categories, and prove additivity, cofinality, devissage and localization theorems – preparing the ground for the theory of higher Grothendieck-Witt groups of schemes as developed in [Sch08a] and [Sch08b]. No assumption on the characteristic is being made.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1865243309999767

Hermitian K -theory of exact categories

We prove a blow-up formula for cyclic homology which we use to show that infinitesimal K-theory satisfies cdh-descent. Combining that result with some computations of the cdh-cohomology of the sheaf of regular functions, we verify a conjecture of Weibel predicting the vanishing of algebraic K-theory of a scheme in degrees less than minus the dimension of the scheme, for schemes essentially of finite type over a field of characteristic zero.

http://annals.math.princeton.edu/wp-content/uploads/annals-v167-n2-p04.pdf

Marco Schlichting

Papers

Idempotent completion of triangulated categories

Negative K -theory of derived categories

Hermitian K-theory, derived equivalences and Karoubi's fundamental theorem

Hermitian K -theory of exact categories

Cyclic homology, cdh-cohomology and negative K-theory