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

인공고관절의 세라믹 볼 헤드의 기계적 안정성 평가를 위한 3 차원 유한요소 해석

Advances in mathematics

Proceedings of the American Mathematical Society

Journal of Algebra

If $f:S' \to S$ is a finite locally free morphism of schemes, we construct a symmetric monoidal "norm" functor $f_\otimes: \mathcal H_*(S') \to\mathcal H_*(S)$, where $\mathcal H_*(S)$ is the pointed unstable motivic homotopy category over $S$. If $f$ is finite etale, we show that it stabilizes to a functor $f_\otimes: \mathcal{SH}(S') \to \mathcal{SH}(S)$, where $\mathcal{SH}(S)$ is the $\mathbb P^1$-stable motivic homotopy category over $S$. Using these norm functors, we define the notion of a normed motivic spectrum, which is an enhancement of a motivic $E_\infty$-ring spectrum. The main content of this text is a detailed study of the norm functors and of normed motivic spectra, and the construction of examples. In particular: we investigate the interaction of norms with Grothendieck's Galois theory, with Betti realization, and with Voevodsky's slice filtration; we prove that the norm functors categorify Rost's multiplicative transfers on Grothendieck-Witt rings; and we construct normed spectrum structures on the motivic cohomology spectrum $H\mathbb Z$, the homotopy K-theory spectrum $KGL$, and the algebraic cobordism spectrum $MGL$. The normed spectrum structure on $H\mathbb Z$ is a common refinement of Fulton and MacPherson's mutliplicative transfers on Chow groups and of Voevodsky's power operations in motivic cohomology.

Norms in motivic homotopy theory

Let X be a Noetherian scheme of finite dimension and denote by rho the (additive inverse of the) morphism in SH(X) from S to Gm corresponding to the unit -1. Here SH(X) denotes the motivic stable homotopy category. We show that the category obtained by inverting rho in SH(X) is canonically equivalent to the (simplicial) local stable homotopy category of the site X_ret, by which we mean the small real etale site of X, comprised of etale schemes over X with the real etale topology. 
One immediate application is that SH(RR)[rho^-1] is equivalent to the classical stable homotopy category. In particular this computes all the stable homotopy sheaves of the rho-local sphere (over RR). As further applications we improve a result of Ananyevskiy-Levine-Panin, reprove a vanishing result of Roendigs and establish some new rigidity results.

Motivic and Real Etale Stable Homotopy Theory

Let be a Noetherian scheme of finite dimension and denote by the (additive inverse of the) morphism corresponding to . Here denotes the motivic stable homotopy category. We show that the category obtained by inverting in is canonically equivalent to the (simplicial) local stable homotopy category of the site , by which we mean the small real etale site of , comprised of etale schemes over with the real etale topology. One immediate application is that is equivalent to the classical stable homotopy category. In particular this computes all the stable homotopy sheaves of the -local sphere (over ). As further applications we show that (improving a result of Ananyevskiy–Levine–Panin), reprove Rondigs’ result that for and establish some new rigidity results.

Motivic and real étale stable homotopy theory

We compute the generalized slices (as defined by Spitzweck–Ostvaer) of the motivic spectrum KO (representing Hermitian K-theory) in terms of motivic cohomology and (a version of) generalized motivic cohomology, obtaining good agreement with the situation in classical topology and the results predicted by Markett–Schlichting. As an application, we compute the homotopy sheaves of (this version of) generalized motivic cohomology, which establishes a version of a conjecture of Morel.

The generalized slices of Hermitian K‐theory

We equate various Euler classes of algebraic vector bundles, including those of [BM, KW, DJK], and one suggested by M.J. Hopkins, A. Raksit, and J.-P. Serre. We establish integrality results for this Euler class, and give formulas for local indices at isolated zeros, both in terms of 6-functor formalism of coherent sheaves and as an explicit recipe in commutative algebra of Scheja and Storch. As an application, we compute the Euler classes associated to arithmetic counts of d-planes on complete intersections in P^n in terms of topological Euler numbers over R and C.

Tom Bachmann

Papers

Norms in motivic homotopy theory

Motivic and Real Etale Stable Homotopy Theory

Motivic and real étale stable homotopy theory

The generalized slices of Hermitian K‐theory

A^1-Euler classes: six functors formalisms, dualities, integrality and linear subspaces of complete intersections