The leray spectral sequence

AbstractThe purpose of this note is to construct a Leray-type spectral sequence for homotopy classes of maps of simplicial presheaves, both stably and unstably, for any morphism of Grothendieck sites. This spectral sequence specializes to the ordinary Leray spectral sequence in sheaf cohomology theory, but may also be used for generalized étale cohomology theories such as étale K-theory

Supercoherence

AbstractThe basic technical point of this paper is that a pseudo-simplicial category can be produced from primitive data consisting of face functors and degeneracy functors, natural isomorphisms corresponding to the standard simplicial identities, and a small list of higher order commutativity conditions relating these isomorphisms. A similar machine exists for constructing contravariant pseudo-functors on Segal's category Γ. Thus, a monoidal category M gives rise canonically to a pseudo-simplicial category BM which enjoys many of the properties of a classifying space construction, while a symmetric monoidal category A determines a Γo category ΓoA which then can be used to directly construct a Γo-space Γo∗A and a spectrum Spt(A). These constructions generalize the basic classical categorical coherence results, and they lead to several applications in homotopy theory and algebraic K-theory. The applications given here include a generalized Quillen S 1S-construction, a pseudo-functional version of the group-completion theorem, an explicit construction to the K-theory and L-theory presheaves of spectra, and a presheaf level delooping of the Q = + theorem

Homotopy colimits and global observables in Abelian gauge theory

We study chain complexes of field configurations and observables for Abelian gauge theory on contractible manifolds, and show that they can be extended to non-contractible manifolds by using techniques from homotopy theory. The extension prescription yields functors from a category of manifolds to suitable categories of chain complexes. The extended functors properly describe the global field and observable content of Abelian gauge theory, while the original gauge field configurations and observables on contractible manifolds are recovered up to a natural weak equivalence

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure

Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety

We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we consider the universal Artin motive mapping to M and denote it ω0X(M). We use this to define a motive

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2,3,4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

Presheaves of symmetric spectra

AbstractIt is shown that the category of presheaves of symmetric spectra on a small Grothendieck site C admits a proper closed simplicial model structure so that the associated homotopy category is adjoint equivalent to the stable category associated to presheaves of spectra on C