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

We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by Aslak Buan, Robert Marsh and Idun Reiten which appeared in their study [8] with M. Reineke and G. Todorov of the link between tilting theory and cluster algebras (cf. also [16]) and a question by Hideto Asashiba about orbit categories. We observe that the resulting triangulated orbit categories provide many examples of triangulated categories with the Calabi-Yau property. These include the category of projective modules over a preprojective algebra of generalized Dynkin type in the sense of Happel-Preiser-Ringel [29], whose triangulated structure goes back to Auslander-Reiten’s work [6], [44], [7].

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On triangulated orbit categories.

In recent years the theory of structured ring spectra (formerly known as A$_{\infty}$- and E$_{\infty}$-ring spectra) has been simplified
 by the discovery of categories of spectra with strictly associative and commutative smash products.
 Now a ring spectrum can simply be defined as a
 monoid with respect to the smash product in one
 of these new categories of spectra. In this paper we provide a general method for constructing model category structures for categories of ring, algebra, and module spectra. This provides the necessary input for obtaining model categories of symmetric ring spectra, functors with smash product, $\Gamma$-rings, and diagram ring spectra.
 Algebraic examples to which our methods apply include the stable module category over the group algebra of a finite group and unbounded chain complexes over a differential graded algebra. 1991 Mathematics Subject Classification: primary 55U35; secondary 18D10.

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Algebras and Modules in Monoidal Model Categories

Working in the category of based spaces, we give the basic theory of diagram spaces and diagram spectra. These are functors for a suitable small topological category . When is symmetric monoidal, there is a smash product that gives the category of -spaces a symmetric monoidal structure. Examples include \begin{enumerate} \item[] prespectra, as defined classically, \item[] symmetric spectra, as defined by Jeff Smith, \item[] orthogonal spectra, a coordinate-free analogue of symmetric spectra with symmetric groups replaced by orthogonal groups in the domain category, \item[] -spaces, as defined by Graeme Segal, \item[] -spaces, an analogue of -spaces with finite sets replaced by finite CW complexes in the domain category. \end{enumerate} We construct and compare model structures on these categories. With the caveat that -spaces are always connective, these categories, and their simplicial analogues, are Quillen equivalent and their associated homotopy categories are equivalent to the classical stable homotopy category. Monoids in these categories are (strict) ring spectra. Often the subcategories of ring spectra, module spectra over a ring spectrum, and commutative ring spectra are also model categories. When this holds, the respective categories of ring and module spectra are Quillen equivalent and thus have equivalent homotopy categories. This allows interchangeable use of these categories in applications.2000 Mathematics Subject Classification: primary 55P42; secondary 18A25, 18E30, 55U35.

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Model categories of diagram spectra

This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and commutative algebra in an abstract monoidal model category, such as derivations, etale and smooth maps, flat and projective modules, etc. We then use the theory of stacks over model categories introduced in \cite{hagI} in order to define a general notion of geometric stack over a base symmetric monoidal model category C, and prove that this notion satisfies the expected properties. The rest of the paper consists in specializing C to several different contexts. First of all, when C=k-Mod is the category of modules over a ring k, with the trivial model structure, we show that our notion gives back the algebraic n-stacks of C. Simpson. Then we set C=sk-Mod, the model category of simplicial k-modules, and obtain this way a notion of geometric derived stacks which are the main geometric objects of Derived Algebraic Geometry. We give several examples of derived version of classical moduli stacks, as for example the derived stack of local systems on a space, of algebra structures over an operad, of flat bundles on a projective complex manifold, etc. Finally, we present the cases where C=(k) is the model category of unbounded complexes of modules over a char 0 ring k, and C=Sp^{\Sigma} the model category of symmetric spectra. In these two contexts, called respectively Complicial and Brave New Algebraic Geometry, we give some examples of geometric stacks such as the stack of associative dg-algebras, the stack of dg-categories, and a geometric stack constructed using topological modular forms.

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Homotopical Algebraic Geometry II: Geometric Stacks and Applications

Introduction and definitions Smallness, limits and constructibility Bousfield localization Brown representability Nilpotence and thick subcategories Noetherian stable homotopy categories Connective stable homotopy theory Semisimple stable homotopy theory Examples of stable homotopy theory Future directions.

Axiomatic stable homotopy theory

MODEL CATEGORIES (Mathematical Surveys and Monographs 63)

Introduction Basic definitions $E$ theory $K$-injective spectra Generalised Moore spectra Bousfield classes The $E(n)$-local category General properties of the $K(n)$-local category Smallness and duality Homology and cohomology functors Brown-Comenetz duality The natural topology Dualisable spectra $K$-nilpotent spectra Grading over the Picard group Examples Questions and conjectures Completion Small objects in other categories References Index.

Neil P. Strickland

Papers

Axiomatic stable homotopy theory

MODEL CATEGORIES (Mathematical Surveys and Monographs 63)

Morava K-Theories and Localisation

Elliptic spectra, the Witten genus and the theorem of the cube

Morava E-theory of symmetric groups