The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

Towers and fibered products of model categories

Given a left Quillen presheaf of localized model structures, we study the homotopy limit model structure on the associated category of sections. We focus specifically on towers and fibered products of model categories. As applications we consider Postnikov towers of model categories, chromatic towers of spectra and Bousfield arithmetic squares of spectra. For spectral model categories, we show that the homotopy fiber of a stable left Bousfield localization is a stable right Bousfield localization

The de Rham homotopy theory and differential graded category

This paper is a generalization of arXiv:0810.0808. We develop the de Rham homotopy theory of not necessarily nilpotent spaces, using closed dg-categories and equivariant dg-algebras. We see these two algebraic objects correspond in a certain way. We prove an equivalence between the homotopy category of schematic homotopy types and a homotopy category of closed dg-categories. We give a description of homotopy invariants of spaces in terms of minimal models. The minimal model in this context behaves much like the Sullivan's minimal model. We also provide some examples. We prove an equivalence between fiberwise rationalizations and closed dg-categories with subsidiary data.Comment: 47 pages. final version. The final publication is available at http://www.springerlink.co

A colimit decomposition for homotopy algebras in Cat

Badzioch showed that in the category of simplicial sets each homotopy algebra of a Lawvere theory is weakly equivalent to a strict algebra. In seeking to extend this result to other contexts Rosicky observed a key point to be that each homotopy colimit in simplicial sets admits a decomposition into a homotopy sifted colimit of finite coproducts, and asked the author whether a similar decomposition holds in the 2-category of categories Cat. Our purpose in the present paper is to show that this is the case.Comment: Some notation changed; small amount of exposition added in intr

Photon Beam Asymmetry Σ for η and η′ Photoproduction From the Proton

Measurements of the linearly-polarized photon beam asymmetry Σ for photoproduction from the proton of η and η ′ mesons are reported. A linearly-polarized tagged photon beam produced by coherent bremsstrahlung was incident on a cryogenic hydrogen target within the CEBAF Large Acceptance Spectrometer. Results are presented for the γ p → η p reaction for incident photon energies from 1.070 to 1.876 GeV, and from 1.516 to 1.836 GeV for the γ p → η ′ p reaction. For γ p → η p , the data reported here considerably extend the range of measurements to higher energies, and are consistent with the few previously published measurements for this observable near threshold. For γ p → η ′ p , the results obtained are consistent with the few previously published measurements for this observable near threshold, but also greatly expand the incident photon energy coverage for that reaction. Initial analysis of the data reported here with the Bonn–Gatchina model strengthens the evidence for four nucleon resonances – the N (1895) 1/2− , N (1900) 3/2+ , N(2100) 1/2+ and N (2120) 3/2− resonances – which presently lack the four-star status in the current Particle Data Group compilation, providing examples of how these new measurements help refine models of the photoproduction process

Variation in inbreeding rates across the range of Northern Spotted Owls (\u3ci\u3eStrix occidentalis caurina\u3c/i\u3e): Insights from over 30 years of monitoring data

Inbreeding has been difficult to quantify in wild populations because of incomplete parentage information. We applied and extended a recently developed framework for addressing this problem to infer inbreeding rates in Northern Spotted Owls (Strix occidentalis caurina) across the Pacific Northwest, USA. Using pedigrees from 14,187 Northern Spotted Owls, we inferred inbreeding rates for 14 types of matings among relatives that produce pedigree inbreeding coefficients of F=0.25 or F=0.125. Inbreeding was most common in the Washington Cascades, where an estimated 15% of individuals are inbred. Inbreeding was lowest in western Oregon (3.5%) and northern California (2.7%), and intermediate for the Olympic Peninsula of Washington (6.1%). Estimates from the Olympic Peninsula were likely underestimates because of small sample sizes and the presence of few pedigrees capable of resolving inbreeding events. Most inbreeding resulted from matings between full siblings or half siblings, although a high rate of inbreeding from mother–son pairs was identified in the Olympic Peninsula. Geographic variation in inbreeding rates may reflect population declines and bottlenecks that have been detected in prior investigations. We show that there is strong selection against inbred birds. Only 3 of 44 inbred birds were later identified as parents (6.8%), whereas 2,823 of 10,380 birds that represented a comparable cross section of the data were later seen as reproducing parents (27.2%). Habitat loss and competition with Barred Owls (S. varia) remain primary threats to Northern Spotted Owls. However, given the negative consequences of inbreeding, Spotted Owl populations in Washington with suitable habitat and manageable numbers of Barred Owls may benefit from translocations of individuals from Oregon and California to introduce new genetic variation and reduce future inbreeding events. La endogamia ha sido dif´ıcil de cuantificar en las poblaciones silvestres debido a la falta de informaci ´on sobre los parentescos. Aplicamos y extendimos un marco conceptual recientemente desarrollado para encarar el problema de inferir las tasas de endogamia en Strix occidentalis caurina a trav´es del noroeste del Pac´ıfico, EEUU. Usando los pedigr´ıes provenientes de 14187 individuos, inferimos las tasas de endogamia para 14 tipos de apareamiento entre parientes que producen coeficientes de endogamia de pedigr´ı de F=0.25 o F=0.125. La endogamia fue ma´s com´un en las Cascadas de Washington, donde se estima que 15% de los individuos son endoga´micos. La endogamia fue menor en el oeste de Oreg´on (3.5%) y el norte de California (2.7%), e intermedia en la Pen´ınsula Ol´ımpica de Washington (6.1%). Las estimaciones de la Pen´ınsula Ol´ımpica fueron probablemente subestimadas debido a los peque ˜nos tama ˜nos de muestreo y a la presencia de pocos pedigr´ıes capaces de resolver los eventos de endogamia. La mayor´ıa de la endogamia result ´o de los apareamientos entre hermanos completos o medios hermanos, aunque se identific ´o una alta tasa de endogamia en parejas madre/hijo en la Pen´ınsula Ol´ımpica. La variaci ´on geogra´ fica en las tasas de endogamia puede reflejar disminuciones poblacionales y cuellos de botella que han sido detectados en investigaciones previas. Mostramos que hay una fuerte selecci ´on contra las aves endoga´micas. Solo tres de 44 aves endoga´micas fueron ma´s tarde identificadas como progenitores (6.8%), mientras que 2823 de 10380 aves que representaron una secci ´on transversal comparable de datos fueron vistas ma´s tarde como progenitores reproductivos (27.2%). La p´erdida de ha´bitat y la competencia con Strix varia sigue siendo la principal amenaza para S. o. caurina. Sin embargo, dadas las consecuencias negativas de la endogamia, las poblaciones de S. occidentalis en Washington con ha´bitat adecuado y n´umeros manejables de Strix varia pueden beneficiarse de traslocaciones de individuos de Oreg´on y California para introducir nueva variaci ´on gen´etica y reducir futuros eventos de endogamia

Comment on the narrow structure reported by Amaryan et al

The CLAS Collaboration provides a comment on the physics interpretation of the results presented in a paper published by M. Amaryan et al. regarding the possible observation of a narrow structure in the mass spectrum of a photoproduction experiment.Comment: to be published in Physical Review

Exploration of hyperfine interaction between constituent quarks via eta productions

In this work, the different exchange freedom, one gluon, one pion or Goldstone boson, in constituent quark model is investigated, which is responsible to the hyperfine interaction between constituent quarks, via the combined analysis of the eta production processes, $\pi^{-}p\rightarrow\eta n$ and $\gamma p\rightarrow\eta p$. With the Goldstone-boson exchange, as well as the one-gluon or one-pion exchange, both the spectrum and observables, such as, the differential cross section and polarized beam asymmetry, are fitted to the suggested values of Particle Data Group and the experimental data. The first two types of exchange freedoms give acceptable description of the spectrum and observables while the one pion exchange can not describe the observables and spectrum simultaneously, so can be excluded. The experimental data for the two processes considered here strongly support the mixing angles for two lowest S11 sates and D13 states as about -30 and 6 degree respectively.Comment: 7 pages, 4 figures, 4 table

Quasi-free photoproduction of η-mesons off 3He nuclei

Quasi-free photoproduction of η-mesons has been measured off nucleons bound in 3He nuclei for incident photon energies from the threshold region up to 1.4 GeV. The experiment was performed at the tagged photon facility of the Mainz MAMI accelerator with an almost 4π covering electromagnetic calorimeter, combining the TAPS and Crystal Ball detectors. The η-mesons were detected in coincidence with the recoil nucleons. This allowed a comparison of the production cross section off quasi-free protons and quasi-free neutrons and a full kinematic reconstruction of the final state, eliminating effects from nuclear Fermi motion. In the S11(1535) resonance peak, the data agree with the neutron/proton cross section ratio extracted from measurements with deuteron targets. More importantly, the prominent structure observed in photoproduction off quasi-free neutrons bound in the deuteron is also clearly observed. Its parameters (width, strength) are consistent with the expectations from the deuteron results. On an absolute scale the cross sections for both quasi-free protons and neutrons are suppressed with respect to the deuteron target pointing to significant nuclear final-state interaction effects