scholarly journals On the density of supercuspidal points of fixed regular weight in local deformation rings and global Hecke algebras

2020 ◽  
Vol 7 ◽  
pp. 337-371 ◽  
Author(s):  
Matthew Emerton ◽  
Vytautas Paškūnas
Keyword(s):  
Hecke Algebras ◽  
Local Deformation ◽  
Deformation Rings

scholarly journals Level 1 Hecke algebras of modular forms modulo 

2014 ◽  
Vol 151 (3) ◽  
pp. 397-415 ◽  
Author(s):  
Joël Bellaïche ◽  
Chandrashekhar Khare
Keyword(s):  
Recent Result ◽  
Modular Forms ◽  
Hecke Algebras ◽  
Local Algebras ◽  
Deformation Rings ◽  
Level 1

AbstractIn this paper, we study the structure of the local components of the (shallow, i.e. without $U_{p}$) Hecke algebras acting on the space of modular forms modulo $p$ of level $1$, and relate them to pseudo-deformation rings. In many cases, we prove that those local components are regular complete local algebras of dimension $2$, generalizing a recent result of Nicolas and Serre for the case $p=2$.

scholarly journals G-valued local deformation rings and global lifts

2019 ◽  
Vol 13 (2) ◽  
pp. 333-378
Author(s):  
Rebecca Bellovin ◽  
Toby Gee
Keyword(s):  
Local Deformation ◽  
Deformation Rings

scholarly journals GLOBALLY REALIZABLE COMPONENTS OF LOCAL DEFORMATION RINGS

2020 ◽  
pp. 1-70
Author(s):  
Frank Calegari ◽  
Matthew Emerton ◽  
Toby Gee
Keyword(s):  
Galois Representations ◽  
Local Deformation ◽  
Deformation Rings ◽  
Galois Deformation

Let $n$ be either  $2$ or an odd integer greater than  $1$ , and fix a prime  $p>2(n+1)$ . Under standard ‘adequate image’ assumptions, we show that the set of components of $n$ -dimensional $p$ -adic potentially semistable local Galois deformation rings that are seen by potentially automorphic compatible systems of polarizable Galois representations over some CM field is independent of the particular global situation. We also (under the same assumption on  $n$ ) improve on the main potential automorphy result of Barnet-Lamb et al. [Potential automorphy and change of weight, Ann. of Math. (2) 179(2) (2014), 501–609], replacing ‘potentially diagonalizable’ by ‘potentially globally realizable’.

scholarly journals Wiles defect for Hecke algebras that are not complete intersections

2021 ◽  
Vol 157 (9) ◽  
pp. 2046-2088
Author(s):  
Gebhard Böckle ◽  
Chandrashekhar B. Khare ◽  
Jeffrey Manning
Keyword(s):  
Hecke Algebras ◽  
Hecke Algebra ◽  
Galois Representation ◽  
Complete Intersections ◽  
Shimura Curves ◽  
Minimal Level ◽  
Quaternion Algebras ◽  
Numerical Criterion ◽  
Maximal Orders ◽  
Deformation Rings

In his work on modularity theorems, Wiles proved a numerical criterion for a map of rings $R\to T$ to be an isomorphism of complete intersections. He used this to show that certain deformation rings and Hecke algebras associated to a mod $p$ Galois representation at non-minimal level are isomorphic and complete intersections, provided the same is true at minimal level. In this paper we study Hecke algebras acting on cohomology of Shimura curves arising from maximal orders in indefinite quaternion algebras over the rationals localized at a semistable irreducible mod $p$ Galois representation $\bar {\rho }$ . If $\bar {\rho }$ is scalar at some primes dividing the discriminant of the quaternion algebra, then the Hecke algebra is still isomorphic to the deformation ring, but is not a complete intersection, or even Gorenstein, so the Wiles numerical criterion cannot apply. We consider a weight-2 newform $f$ which contributes to the cohomology of the Shimura curve and gives rise to an augmentation $\lambda _f$ of the Hecke algebra. We quantify the failure of the Wiles numerical criterion at $\lambda _f$ by computing the associated Wiles defect purely in terms of the local behavior at primes dividing the discriminant of the global Galois representation $\rho _f$ which $f$ gives rise to by the Eichler–Shimura construction. One of the main tools used in the proof is Taylor–Wiles–Kisin patching.

Electron microscopy investigations on the mineral lorándite (TlAsS2) from Allchar in Macedonia

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tobias Necke ◽  
Maximilian Trapp ◽  
Stefan Lauterbach ◽  
Georg Amthauer ◽  
Hans-Joachim Kleebe
Keyword(s):  
Electron Microscopy ◽  
Single Crystals ◽  
Secondary Phase ◽  
Lattice Energy ◽  
Local Deformation ◽  
Crystal Defects ◽  
Coffee Bean ◽  
Electron Dose ◽  
Chemical Difference ◽  
Natural Mineral

Abstract In this paper, we report on electron microscopy studies of single crystals of the natural mineral lorándite, TlAsS2. The main focus of this investigation was to address the question as to whether those lorándite crystals are chemically and structurally homogeneous, in order to be utilized as an effective neutrino detector within the lorándite experiment (LOREX) project. Apart from few secondary minerals, being present only at the surface of the lorándite samples, scanning electron microscopy (SEM) indicated homogeneous crystals. Similarly, transmission electron microscopy (TEM) imaging revealed a homogenous and undisturbed crystal structure, with the only exception of local coffee-bean contrasts; however, rarely observed. These specific contrast variations are known to be a typical strain indicator caused by a local deformation of the crystal lattice. Energy-dispersive X-ray spectroscopy (EDS) in conjunction with electron energy-loss spectroscopy (EELS) did not show any significant chemical difference when analysing regions on or off those coffee-bean features, indicating a chemically homogenous mineral. Since the presence of lattice disturbing secondary phase precipitates could be excluded by imaging and complementary chemical analysis, crystal defects such as dislocations and stacking faults or minor fluid inclusions are discussed as the probable origin of this local elastic strain. The experimental results confirm that the studied lorándite single crystals fulfil all structural and chemical requirements to be employed as the natural mineral that allows to determine solar neutrino fluxes. In addition, critical issues regarding the rather challenging sample preparation of lorándite are reported and a quantification of the maximum tolerable electron dose in the TEM is presented, since lorándite was found to be sensitive with respect to electron beam irradiation. Furthermore, the limits of EDS measurements due to peak overlapping are shown and discussed utilizing the case of Pb in lorándite. In this regard, a comparison with the Tl- and Pb-containing natural mineral hutchinsonite, TlPbAs5S9, is also included.

scholarly journals Design and Calibration of Robot Base Force/Torque Sensors and Their Application to Non-Collocated Admittance Control for Automated Tool Changing

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 2895
Author(s):  
Hubert Gattringer ◽  
Andreas Müller ◽  
Philip Hoermandinger
Keyword(s):  
Steel Plate ◽  
Robotic Manipulators ◽  
Indirect Measurement ◽  
Local Deformation ◽  
Contact Forces ◽  
The Novel ◽  
Admittance Control ◽  
Load Cells ◽  
Series Elastic Actuators ◽  
Automated Tool

Robotic manipulators physically interacting with their environment must be able to measure contact forces/torques. The standard approach to this end is attaching force/torque sensors directly at the end-effector (EE). This provides accurate measurements, but at a significant cost. Indirect measurement of the EE-loads by means of torque sensors at the actuated joint of a robot is an alternative, in particular for series-elastic actuators, but requires dedicated robot designs and significantly increases costs. In this paper, two alternative sensor concept for indirect measurement of EE-loads are presented. Both sensors are located at the robot base. The first sensor design involves three load cells on which the robot is mounted. The second concept consists of a steel plate with four spokes, at which it is suspended. At each spoke, strain gauges are attached to measure the local deformation, which is related to the load at the sensor plate (resembling the main principle of a force/torque sensor). Inferring the EE-load from the so determined base wrench necessitates a dynamic model of the robot, which accounts for the static as well as dynamic loads. A prototype implementation of both concepts is reported. Special attention is given to the model-based calibration, which is crucial for these indirect measurement concepts. Experimental results are shown when the novel sensors are employed for a tool changing task, which to some extend resembles the well-known peg-in-the-hole problem.

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