Local-global principles for homogeneous spaces over some two-dimensional geometric global fields

In this article, we study the obstructions to the local-global principle for homogeneous spaces with connected or abelian stabilizers over finite extensions of the field ℂ ⁢ ( ( x , y ) ) {\mathbb{C}((x,y))} of Laurent series in two variables over the complex numbers and over function fields of curves over ℂ ⁢ ( ( t ) ) {\mathbb{C}((t))} . We give examples that prove that the Brauer–Manin obstruction with respect to the whole Brauer group is not enough to explain the failure of the local-global principle, and we then construct a variant of this obstruction using torsors under quasi-trivial tori which turns out to work. In the end of the article, we compare this new obstruction to the descent obstruction with respect to torsors under tori. For that purpose, we use a result on towers of torsors, that is of independent interest and therefore is proved in a separate appendix.

Inverse modeling of halocarbons: sensitivity to the baseline definition

<p>The identification of the baseline is an important task in inverse modeling of greenhouse gases, as it represents the influence of atmospheric chemistry and transport and surface fluxes from outside the inversion domain, or flux contributions prior to the length of the backward calculation for Lagrangian models. When modeling halocarbons, observation-based approaches are often used to calculate the baseline, although model-based approaches are an alternative. Model-based methods need global unbiased fields of mixing ratios of the observed species, which are not always easy to get and which need to be interfaced with the model used for the inversion. To find the best way to identify the baseline and to investigate whether the usage of observation-based approaches is suitable for inverse modeling of halocarbons, we use and analyze a model-based and two frequently used observation-based methods to determine the baseline and investigate their influence on inversion results. The model-based method couples global fields of mixing ratios with backwards-trajectories at their point of termination. We simulate those global fields with a Lagrangian particle dispersion model, FLEXPART_CTM, that uses a nudging routine to relax model data to observed values. The second method under investigation is the robust estimation of baseline signal (REBS) method, that is purely based on statistical analysis of observations. The third analyzed method is also primarily observation-based, but uses model information to subtract prior simulated mixing ratios from selected observations. We apply those three methods to sulfur hexafluoride (SF<sub>6</sub>) and use the Bayesian inversion framework FLEXINVERT for the inverse modeling and the Lagrangian particle dispersion model FLEXPART to calculate the source-receptor-relationship used in the inversion.</p>

Branching laws for classical groups: the non-tempered case

This paper generalizes the Gan–Gross–Prasad (GGP) conjectures that were earlier formulated for tempered or more generally generic L-packets to Arthur packets, especially for the non-generic L-packets arising from Arthur parameters. The paper introduces the key notion of a relevant pair of Arthur parameters that governs the branching laws for ${{\rm GL}}_n$ and all classical groups over both local fields and global fields. It plays a role for all the branching problems studied in Gan et al. [Symplectic local root numbers, central critical L-values and restriction problems in the representation theory of classical groups. Sur les conjectures de Gross et Prasad. I, Astérisque 346 (2012), 1–109] including Bessel models and Fourier–Jacobi models.