scholarly journals The decomposition group of a line in the plane

2017 ◽  
Vol 145 (9) ◽  
pp. 3665-3680
Author(s):  
Isac Hedén ◽  
Susanna Zimmermann
Keyword(s):  
Decomposition Group

scholarly journals Autonomic Modulation During Baseline and Recovery Sleep in Adult Sleepwalkers

2021 ◽  
Vol 12 ◽  
Author(s):  
Geneviève Scavone ◽  
Andrée-Ann Baril ◽  
Jacques Montplaisir ◽  
Julie Carrier ◽  
Alex Desautels ◽  
...  
Keyword(s):  
Heart Rate ◽  
Sleep Deprivation ◽  
Slow Wave ◽  
Slow Wave Sleep ◽  
Low Frequency ◽  
Medium Effect ◽  
Sleep Cycle ◽  
Autonomic Modulation ◽  
Decomposition Group ◽  
Recovery Sleep

Sleepwalking has been conceptualized as deregulation between slow-wave sleep and arousal, with its occurrence in predisposed patients increasing following sleep deprivation. Recent evidence showed autonomic changes before arousals and somnambulistic episodes, suggesting that autonomic dysfunctions may contribute to the pathophysiology of sleepwalking. We investigated cardiac autonomic modulation during slow-wave sleep in sleepwalkers and controls during normal and recovery sleep following sleep deprivation. Fourteen adult sleepwalkers (5M; 28.1 ± 5.8 years) and 14 sex- and age-matched normal controls were evaluated by video-polysomnography for one baseline night and during recovery sleep following 25 h of sleep deprivation. Autonomic modulation was investigated with heart rate variability during participants' slow-wave sleep in their first and second sleep cycles. 5-min electrocardiographic segments from slow-wave sleep were analyzed to investigate low-frequency (LF) and high-frequency (HF) components of heart rate spectral decomposition. Group (sleepwalkers, controls) X condition (baseline, recovery) ANOVAs were performed to compare LF and HF in absolute and normalized units (nLF and nHF), and LF/HF ratio. When compared to controls, sleepwalkers' recovery slow-wave sleep showed lower LF/HF ratio and higher nHF during the first sleep cycle. In fact, compared to baseline recordings, sleepwalkers, but not controls, showed a significant decrease in nLF and LF/HF ratio as well as increased nHF during recovery slow-wave sleep during the first cycle. Although non-significant, similar findings with medium effect sizes were observed for absolute values (LF, HF). Patterns of autonomic modulation during sleepwalkers' recovery slow-wave sleep suggest parasympathetic dominance as compared to baseline sleep values and to controls. This parasympathetic predominance may be a marker of abnormal neural mechanisms underlying, or interfere with, the arousal processes and contribute to the pathophysiology of sleepwalking.

Computation of the Decomposition Group of a Triangular Ideal

2004 ◽  
Vol 15 (3-4) ◽  
pp. 279-294 ◽  
Author(s):  
I. Abdeljaouad-Tej ◽  
S. Orange ◽  
G. Renault ◽  
A. Valibouze
Keyword(s):  
Decomposition Group

scholarly journals -INVARIANTS AND LOCAL–GLOBAL COMPATIBILITY FOR THE GROUP

2016 ◽  
Vol 4 ◽  
Author(s):  
YIWEN DING
Keyword(s):  
Real Number ◽  
Number Field ◽  
Cohomology Group ◽  
Shimura Curves ◽  
Langlands Correspondence ◽  
Decomposition Group ◽  
Étale Cohomology ◽  
Totally Real ◽  
Local Langlands Correspondence ◽  
Real Number Field

Let $F$ be a totally real number field, ${\wp}$ a place of $F$ above $p$. Let ${\it\rho}$ be a $2$-dimensional $p$-adic representation of $\text{Gal}(\overline{F}/F)$ which appears in the étale cohomology of quaternion Shimura curves (thus ${\it\rho}$ is associated to Hilbert eigenforms). When the restriction ${\it\rho}_{{\wp}}:={\it\rho}|_{D_{{\wp}}}$ at the decomposition group of ${\wp}$ is semistable noncrystalline, one can associate to ${\it\rho}_{{\wp}}$ the so-called Fontaine–Mazur ${\mathcal{L}}$-invariants, which are however invisible in the classical local Langlands correspondence. In this paper, we prove one can find these ${\mathcal{L}}$-invariants in the completed cohomology group of quaternion Shimura curves, which generalizes some of Breuil’s results [Breuil, Astérisque, 331 (2010), 65–115] in the $\text{GL}_{2}/\mathbb{Q}$-case.

scholarly journals Self-dual integral normal bases and Galois module structure

2013 ◽  
Vol 149 (7) ◽  
pp. 1175-1202 ◽  
Author(s):  
Erik Jarl Pickett ◽  
Stéphane Vinatier
Keyword(s):  
Number Fields ◽  
Local Fields ◽  
Module Structure ◽  
Galois Module ◽  
Local Norm ◽  
Normal Bases ◽  
Decomposition Group ◽  
Rings Of Integers ◽  
Odd Degree ◽  
Exponential Power

AbstractLet $N/ F$ be an odd-degree Galois extension of number fields with Galois group $G$ and rings of integers ${\mathfrak{O}}_{N} $ and ${\mathfrak{O}}_{F} = \mathfrak{O}$. Let $ \mathcal{A} $ be the unique fractional ${\mathfrak{O}}_{N} $-ideal with square equal to the inverse different of $N/ F$. B. Erez showed that $ \mathcal{A} $ is a locally free $\mathfrak{O}[G] $-module if and only if $N/ F$ is a so-called weakly ramified extension. Although a number of results have been proved regarding the freeness of $ \mathcal{A} $ as a $ \mathbb{Z} [G] $-module, the question remains open. In this paper we prove that $ \mathcal{A} $ is free as a $ \mathbb{Z} [G] $-module provided that $N/ F$ is weakly ramified and under the hypothesis that for every prime $\wp $ of $\mathfrak{O}$ which ramifies wildly in $N/ F$, the decomposition group is abelian, the ramification group is cyclic and $\wp $ is unramified in $F/ \mathbb{Q} $. We make crucial use of a construction due to the first author which uses Dwork’s exponential power series to describe self-dual integral normal bases in Lubin–Tate extensions of local fields. This yields a new and striking relationship between the local norm-resolvent and the Galois Gauss sum involved. Our results generalise work of the second author concerning the case of base field $ \mathbb{Q} $.

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