Bounded derived categories of very simple manifolds

An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical terms. This is a partial generalization of an impressive result due to Bondal and Van den Bergh.Comment: 11 pages one important references is added, proof of lemma 2.1 (2) and many typos are correcte

A Generalization of Martin's Axiom

We define the $\aleph_{1.5}$ chain condition. The corresponding forcing axiom is a generalization of Martin's Axiom and implies certain uniform failures of club--guessing on $\omega_1$ that don't seem to have been considered in the literature before.Comment: 36 page

Gas-phase molecular structure of nopinone and its water complexes studied by microwave fourier transform spectroscopy and quantum chemical calculations

Several monoterpenes and terpenoids are biogenic volatile organic compounds which are emitted in the atmosphere, where they react with OH, O$_3$ and NO$_x$ etc. to give rise to several oxidation and degradation products.\footnote{A. Calogirou, B.R. Larsen, and D. Kotzias, \textit{ Atmospheric Environment}, \textbf{33}, 1423-1439, (1999).} Their decomposition products are a major source of secondray organic aerosol (SOA).\footnote{P. Paasonen et al., \textit{Nat. Geosci.}, \textbf{6}, 438-442 (2013)} Spectroscopic information on these atmospheric species is still very scarce. The rotational spectrum of nopinone (C$_9$H$_{14}$O) one of the major oxidation products of $\beta$-pinene,\footnote{D. Zhang and R. Zhang \textit{The Journal of Chemical Physics}, \textbf{122}, 114308, (2005).} \footnote{R. Winterhalter et al. \textit{ Journal of Atmospheric Chemistry}, \textbf{35}, 165-197, (2000).} and of its water complexes were recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. The structure of the unique stable conformer of the nopinone was optimized using density functional theory and \textit{ab initio} calculations. Signals from the parent species and from the $^{13}C$ and $^{18}O$ isotopomers were observed in natural abundance. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled. \\ The structures of several conformers of the nopinone-water complexes with up to three molecules of water were optimized using density functional theory and \textit{ab initio} calculations. The energetically most stable of calculated conformers were observed and anlyzed. The rotational and centrifugal distortion parameters were fitted to a Watson’s Hamiltonian in the A-reduction. The present work provides the first spectroscopic characterization of nopinone and its water complexes in the gas phase.\

The structure and molecular parameters of camphene determined by fourier transform microwave spectroscopy and quantum chemical calculations

The emission of volatile organic compounds, from plants has strong revelance for plant physiology, plant ecology and atmospheric chemistry.\footnote{R. Baraldi, F. Rapparini, O. Facini, D. Spano and P. Duce, \textit{ Journal of Mediterranean Ecology}, \textbf{Vol.6}, No.1, (2005).} Camphene (C$_{10}$H$_{16}$) is a bicyclic monoterpene which is emitted in the atmosphere by biogenic sources.\footnote{A. Bracho-Nunez, N. M. Knothe, S. Welter, M. Staudt, W. R. Costa, M. A. R. Liberato, M. T. F. Piedade, and J. Kesselmeier \textit{ Biogeosciences}, \textbf{10}, 5855-5873, (2013).}\footnote{Minna Kivim\"{a}enp\"{a}\"{a}, Narantsetseg Magsarjav, Rajendra Ghimire, Juha-Matti Markkanen, Juha Heijari, Martti Vuorinen and Jarmo K. Holopainen, \textit{Atmospheric Environment}, \textbf{60}, 477-485, (2012).} The structure of the unique stable conformer was optimized using density functional theory and \textit{ab initio} calculations. The rotational spectrum of camphene was recorded in a supersonic jet expansion with a Fourier transform microwave spectrometer over the range 2-20 GHz. Signals from the parent species and from the ten $^{13}C$ isotopomers were observed in natural abundance. The rotational and centrifugal distortion parameters were fitted to a Watson’s Hamiltonian in the A-reduction. A magnetic hyperfine structure associated with the pairs of hydrogen nuclei in the methylene groups was observed and modeled.\\ The rotational constants coupled to the equilibrium structure calculations were used to determine the r$_0$ and the r$_m^{(1)}$ gas-phase geometries of the carbon skeleton. The present work provides the first spectroscopic characterization of camphene in the gas phase and these results are also relevant for ozonolysis kinetics study through Criegee intermediates.\footnote{R.C. de M. Oliveira and G. F. Bauerfeldt, \textit{J. Phys. Chem. A}, \textbf {119} 2802-2812 (2015).}\

Gorenstein homological algebra and universal coefficient theorems

We study criteria for a ring—or more generally, for a small category—to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman’s Brown–Adams representability theorem for compactly generated categories

Cohomological descent theory for a morphism of stacks and for equivariant derived categories

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As a corollary, we show that for an action of a reductive group on a scheme, the derived category of equivariant sheaves is equivalent to the category of objects, equipped with an action of the group, in the ordinary derived category.Comment: 28 page

The Baum-Connes Conjecture via Localisation of Categories

We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant homology theories, not just for the K-theory of the crossed product. We extend many of the known techniques for proving the Baum-Connes conjecture to this more general setting

Azumaya Objects in Triangulated Bicategories

We introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring. We go on to describe triangulated bicategories and prove a characterization theorem for Azumaya objects therein. This theory applies to give a homotopical Brauer group for derived categories of rings and ring spectra. We show that the homotopical Brauer group of an Eilenberg-Mac Lane spectrum is isomorphic to the homotopical Brauer group of its underlying commutative ring. We also discuss tilting theory as an application of invertibility in triangulated bicategories.Comment: 23 pages; final version; to appear in Journal of Homotopy and Related Structure