First steps towards pp-adic Langlands functoriality

By the theory of Colmez and Fontaine, a de Rham representation of the Galois group of a local field roughly corresponds to a representation of the Weil-Deligne group equipped with an admissible filtration on the underlying vector space. Using a modification of the classical local Langlands correspondence, we associate with any pair consisting of a Weil-Deligne group representation and a type of a filtration (admissible or not) a specific locally algebraic representation of a general linear group. We advertise the conjecture that this pair comes from a de Rham representation if and only if the corresponding locally algebraic representation carries an invariant norm. In the crystalline case, the Weil-Deligne group representation is unramified and the associated locally algebraic representation can be studied using the classical Satake isomorphism. By extending the latter to a specific norm completion of the Hecke algebra, we show that the existence of an invariant norm implies that our pair, indeed, comes from a crystalline representation. We also show, by using the formalism of Tannakian categories, that this latter fact is compatible with classical unramified Langlands functoriality and therefore generalizes to arbitrary split reductive groups

An adjunction formula for the Emerton-Jacquet functor

The Emerton–Jacquet functor is a tool for studying locally analytic representations of p-adic Lie groups. It provides a way to access the theory of p-adic automorphic forms. Here we give an adjunction formula for the Emerton–Jacquet functor, relating it directly to locally analytic inductions, under a strict hypothesis that we call non-critical. We also further study the relationship to socles of principal series in the non-critical setting

Marine Protected Areas: Country Case Studies on Policy, Governance and Institutional Issues

This document presents case studies of the policy, governance and institutional issues of marine protected areas (MPAs) in South America (Northeastern)-Brazil; India, Palau and Senegal. It is the first of four in a global series of case studies on MPAs. An initial volume provides a synthesis and analysis of all the studies. The set of global MPA case studies was designed to close a deficit in information on the governance of MPAs and spatial management tools, within both fisheries management and biodiversity conservation contexts. The studies examine governance opportunities in and constraints on the use of spatial management measures at the national level. They were also designed to inform implementation of the FAO Technical Guidelines on marine protected areas (MPAs) and fisheries, which were developed to provide information and guidance on the use of MPAs in the context of fisheries

The classification of irreducible admissible mod p representations of a p-adic GL_n

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the classification of irreducible admissible smooth GL_n(F)-representations over \bar F_p in terms of supersingular representations. As a consequence we deduce that supersingular is the same as supercuspidal. These results generalise the work of Barthel-Livne for n = 2. For general split reductive groups we obtain similar results under stronger hypotheses.Comment: 55 pages, to appear in Inventiones Mathematica

Even Galois Representations and the Fontaine--Mazur conjecture II

We prove, under mild hypotheses, that there are no irreducible two-dimensional_even_ Galois representations of \Gal(\Qbar/\Q) which are de Rham with distinct Hodge--Tate weights. This removes the "ordinary" hypothesis required in previous work of the author. We construct examples of irreducible two-dimensional residual representations that have no characteristic zero geometric (= de Rham) deformations.Comment: Updated to take into account suggestions of the referee; the main theorems remain unchange

Resveratrol content of two Californian table grape cultivars

Research Note

Universal deformation rings for the symmetric group S_4

Let k be an algebraically closed field of characteristic 2, and let W be the ring of infinite Witt vectors over k. Let S_4 denote the symmetric group on 4 letters. We determine the universal deformation ring R(S_4,V) for every kS_4-module V which has stable endomorphism ring k and show that R(S_4,V) is isomorphic to either k, or W[t]/(t^2,2t), or the group ring W[Z/2]. This gives a positive answer in this case to a question raised by the first author and Chinburg whether the universal deformation ring of a representation of a finite group with stable endomorphism ring k is always isomorphic to a subquotient ring of the group ring over W of a defect group of the modular block associated to the representation.Comment: 12 pages, 2 figure

Color Improves Edge Classification

Meeting AbstractCopyright 2019 The Author(s). Our visual environment contains both luminance and color (chromatic) information. Understanding the role that each plays in our visual perception of natural scenes is a continuing topic of investigation. In this study, we explore the role that color cues play in a specific task: edge classification. Despite the complexity of the visual world, humans rarely confuse variations in illumination, for example, shadows, from variations in material properties, for example, paint or stain. This ability to distinguish illumination from material edges is crucial for determining the spatial layout of objects and surfaces in natural scenes. Color is believed to be a useful cue to this categorization, given that most color changes tend to be material in origin, whereas luminance changes tend to be either material or illumination in origin. We conducted a psychophysical experiment that required subjects to classify edges as “shadow” or “other,” for images containing or not color information. We found edge classification performance to be superior for the color compared with grayscale images. We also defined machine observers sensitive to simple image properties and found that they too classified the edges better with color information. Our results show that color acts as a cue for edge classification in images of natural scenes

Color improves edge classification in human vision

Data Availability Statement: All relevant data are within the manuscript and its Supporting Information files.© 2019 Breuil et al. Despite the complexity of the visual world, humans rarely confuse variations in illumination, for example shadows, from variations in material properties, such as paint or stain. This ability to distinguish illumination from material edges is crucial for determining the spatial layout of objects and surfaces in natural scenes. In this study, we explore the role that color (chromatic) cues play in edge classification. We conducted a psychophysical experiment that required subjects to classify edges into illumination and material, in patches taken from images of natural scenes that either contained or did not contain color information. The edge images were of various sizes and were pre-classified into illumination and material, based on inspection of the edge in the context of the whole image from which the edge was extracted. Edge classification performance was found to be superior for the color compared to grayscale images, in keeping with color acting as a cue for edge classification. We defined machine observers sensitive to simple image properties and found that they too classified the edges better with color information, although they failed to capture the effect of image size observed in the psychophysical experiment. Our findings are consistent with previous work suggesting that color information facilitates the identification of material properties, transparency, shadows and the perception of shape-from-shading.IDEX; Canadian Institute of Health. The study was supported by a travel grant from IDEX given to CB and a Canadian Institute of Health Research grant #MOP 123349 given to FK. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript