The non-equivariant coherent-constructible correspondence and a conjecture of King

The coherent-constructible (CC) correspondence is a relationship between coherent sheaves on a toric variety X and constructible sheaves on a real torus $$mathbb {T}$$T. This was discovered by Bondal and established in the equivariant setting by Fang, Liu, Treumann, and Zaslow. In this paper, we explore various aspects of the non-equivariant CC correspondence. Also, we use the non-equivariant CC correspondence to prove the existence of tilting complexes in the derived categories of toric orbifolds satisfying certain combinatorial conditions. This has applications to a conjecture of King

Pliocene to Quaternary deformation in the Var Basin (Nice, SE France) and its interpretation in terms of "slow-active" faulting

International audienceSeismic hazard assessment of active faults in slow orogenic domains is a challenging issue. In this paper we present a multi-disciplinary approach based on a Digital Elevation Model (DEM), 3D-geological modelling, fracture analysis, and strain analysis of pebbles in a Pliocene molasse basin. The basin is cross-cut by "slow-active" faults of the Donaréo and St Blaise-Aspremont fault system. The DEM shows a topographic disturbance emphasized by slope gradients and the drainage system, which is ascribed to the Plio-Quaternary fault trace. Fracturation analysis evidences two fault corridors oriented approximately N150°E and N20°E. Paleo-stress analysis provides orientations similar to those derived from the focal mechanisms of current regional seismicity, with the main stress σ1 oriented N20°E and a (σ2 − σ3)/(σ1 − σ3) ratio of 0.31. The σ2 versus σ3 permutations are in agreement with ongoing strike-slip deformation at least since the early Pliocene. Discontinuous fracturation and comparison with seismic monitoring on regional active fault zones suggest that shallow seismicity may be expressed by low-magnitude (Mw < 4) seismic swarms. Deformation of pebbles occurs mainly by pressure-dissolution processes. Pebble striation orientations show a bimodal distribution, parallel to the two fault strands. Pebble deformation and the paucity of striated surfaces along the main faults suggests rare seismic deformation and long-lasting aseismic creep processes. Geometrical 3D analysis shows the formation and migration of a Plio-Quaternary basin about 500 metres east of the main fault system, together with folding and tilting of the post-Messinian Pliocene molasse. These observations indicate that the fault remained active from the Pliocene to the Quaternary, and possibly up to the present time. However, the estimates of the minimum slip rate on the faults of about 0.02 mm a−1 vertical and 0.03 mm a−1 horizontal are unlikely to produce any significant high-magnitude earthquakes, but rather swarm-like low-magnitude seismicity with long temporal recurrence

La montagne, laboratoire du changement climatique

La montagne est un territoire d’exception, réservoir de multiples ressources (bois, minerais, eau, énergie, neige, etc.), mais qui doit composer avec des handicaps naturels (pente, altitude et climat). Elle s’est ainsi construite au fil de son histoire une place spécifique au sein de l’Aménagement du territoire (RTM, Plan neige, loi « Montagne »). La question du changement climatique s’ajoute aujourd'hui aux réflexions et aux pratiques d’aménagement. Il faut alors s’interroger sur les implications de la rencontre entre un objet aux spécificités marquées et un phénomène générique, dont la représentation découle d’une appréhension globale du climat (réchauffement planétaire ou global warming) à travers des modèles prospectifs sans finesses dans leurs projections locales. L’objectif de ce numéro thématique de la RGA est d’explorer cette rencontre selon quatre domaines particuliers : écosystèmes de montagne, agropastoralisme, forêt et sylviculture, risques – naturels et économiques. Il s’agit dans ce cadre de tester l’hypothèse selon laquelle, dans un contexte marqué par le spectre du changement climatique, le droit à l’expérimentation défendu par les élus montagnards prend une dimension nouvelle, faisant de la montagne un laboratoire de l’Aménagement du territoire. Mountain areas are exceptional environments, endowed with a wide variety of natural resources (wood, minerals, water, energy, snow, etc.), but at the same time having to deal with a number of natural handicaps (slope, altitude and climate). Over the years, mountain areas have thus come to occupy a special place in spatial planning and development (RTM (Mountain Terrain Restoration programme), Plan neige (winter resort development programme), Loi Montagne (Mountain Act)). A further concern today for planners and decision-makers is the question of climate change. It is therefore important to examine the implications of the interaction between an object, the mountain area, with its distinctive characteristics and a generic phenomenon, the representation of which stems from a global understanding of climate (global warming) obtained through general prospective models, models that need to be more refined in their projections at the local level. The objective of this special issue of the RGA is to explore this interaction in terms of four special areas: mountain ecosystems, agropastoralism, forests and forestry, and natural and economic risks. This framework provides the opportunity to test the hypothesis that in a context haunted by the spectre of climate change, the right to experimentation defended by the elected representatives of mountain areas takes on a new dimension, making mountain areas a laboratory for spatial planning

Descent of vector bundles under wildly ramified extensions

Given an irreducible normal Noetherian scheme and a finite Galois extension of the field of rational functions, we discuss the comparison of the categories of vector bundles on the scheme and equivariant vector bundles on the integral closure in the extension. This is well understood in the tame case (geometric stabilizer groups of order invertible in the local rings), so we focus on the wild (non-tame) case, which may be reduced to the case of cyclic extensions of prime order. In this case, under an additional flatness hypothesis, we give a characterization of the equivariant vector bundles that arise by base change from vector bundles on the scheme