scholarly journals Galois deformation theory for norm fields and flat deformation rings

2011 ◽  
Vol 131 (7) ◽  
pp. 1258-1275
Author(s):  
Wansu Kim
Keyword(s):  
Deformation Theory ◽  
Deformation Rings ◽  
Galois Deformation

scholarly journals DEFORMATION CONDITIONS FOR PSEUDOREPRESENTATIONS

2019 ◽  
Vol 7 ◽  
Author(s):  
PRESTON WAKE ◽  
CARL WANG-ERICKSON
Keyword(s):  
Stability Condition ◽  
Deformation Theory ◽  
Axiomatic Definition ◽  
Galois Deformation ◽  
Definition Of

Given a property of representations satisfying a basic stability condition, Ramakrishna developed a variant of Mazur’s Galois deformation theory for representations with that property. We introduce an axiomatic definition of pseudorepresentations with such a property. Among other things, we show that pseudorepresentations with a property enjoy a good deformation theory, generalizing Ramakrishna’s theory to pseudorepresentations.

scholarly journals $G$-valued Galois deformation rings when $\ell \neq p$

2019 ◽  
Vol 26 (4) ◽  
pp. 973-990
Author(s):  
Jeremy Booher ◽  
Stefan Patrikis
Keyword(s):  
Deformation Rings ◽  
Galois Deformation

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 Derived Galois deformation rings

2018 ◽  
Vol 327 ◽  
pp. 470-623 ◽  
Author(s):  
S. Galatius ◽  
A. Venkatesh
Keyword(s):  
Deformation Rings ◽  
Galois Deformation

Theoretical and experimental research on slip and uplift of the timber-concrete composite beam

BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Deformation Theory ◽  
Concrete Slab ◽  
Theoretical Calculations ◽  
Structural Element ◽  
Structural Efficiency ◽  
Theoretical Investigations ◽  
New Type ◽  
Interlayer Slip ◽  
Good Agreement

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.

Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Phase Field ◽  
Deformation Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Rectangular Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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