The Schur multiplier of finite symplectic groups

We show that the Schur multiplier of $Sp(2g,\mathbb Z/D\mathbb Z)$ is $\mathbb Z/2\mathbb Z$, when $D$ is divisible by 4.Comment: Bull. Soc. Math. France, to appea

Hochster duality in derived categories and point-free reconstruction of schemes

For a commutative ring $R$, we exploit localization techniques and point-free topology to give an explicit realization of both the Zariski frame of $R$ (the frame of radical ideals in $R$) and its Hochster dual frame, as lattices in the poset of localizing subcategories of the unbounded derived category $D(R)$. This yields new conceptual proofs of the classical theorems of Hopkins-Neeman and Thomason. Next we revisit and simplify Balmer's theory of spectra and supports for tensor triangulated categories from the viewpoint of frames and Hochster duality. Finally we exploit our results to show how a coherent scheme $(X,\mathcal{O}_X)$ can be reconstructed from the tensor triangulated structure of its derived category of perfect complexes.Comment: v5:Minoir typos corrected the proof of tensor nilpotence is made totally point-free and self-contained; some simplifications and expository improvements; section on preliminaries shortened; 50pp. To appear in Trans. AM

Homology fibrations and "group-completion" revisited

We give a proof of the Jardine-Tillmann generalized group completion theorem. It is much in the spirit of the original homology fibration approach by McDuff and Segal, but follows a modern treatment of homotopy colimits, using as little simplicial technology as possible. We compare simplicial and topological definitions of homology fibrations.Comment: 13 page

Effect of Dynamic Surface Polarization on the Oxidative Stability of Solvents in Nonaqueous Li-O2_2 Batteries

Polarization-induced renormalization of the frontier energy levels of interacting molecules and surfaces can cause significant shifts in the excitation and transport behavior of electrons. This phenomenon is crucial in determining the oxidative stability of nonaqeous electrolytes in high energy density electrochemical systems such as the Li-O$_2$ battery. On the basis of partially self-consistent first-principles ScGW0 calculations, we systematically study how the electronic energy levels of four commonly used solvent molecules, namely dimethylsulfoxide (DMSO), dimethoxyethane (DME), tetrahydrofuran (THF) and acetonitrile (ACN), renormalize when physisorbed on the different stable surfaces of Li$_2$O$_2$, the main discharge product. Using band level alignment arguments, we propose that the difference between the solvent's highest occupied molecular orbital (HOMO) level and the surface's valence band maximum (VBM) is a refined metric of oxidative stability. This metric and a previously used descriptor, solvent's gas phase HOMO level, agree quite well for physisorbed cases on pristine surfaces where ACN is oxidatively most stable followed by DME, THF and DMSO. However, this effect is intrinsically linked to the surface chemistry of solvent's interaction with the surfaces states and defects, and depends strongly on their nature. We conclusively show that the propensity of solvent molecules to oxidize will be significantly higher on Li$_2$O$_2$ surfaces with defects as compared to pristine surfaces. This suggests that the oxidatively stability of solvent is dynamic and is a strong function of surface electronic properties. Thus, while gas phase HOMO levels could be used for preliminary solvent candidate screening, a more refined picture of solvent stability requires mapping out the solvent stability as a function of the state of the surface under the operating conditions.Comment: 10 Pages, 8 Figure