The proof of peterson's conjecture for GL(2) over a global field of characteristic p

1988 ◽  
Vol 22 (1) ◽  
pp. 28-43 ◽  
Author(s):  
V. G. Drinfel'd
Keyword(s):  
Global Field ◽  
Characteristic P

scholarly journals CONTROL THEOREMS FOR ELLIPTIC CURVES OVER FUNCTION FIELDS

2009 ◽  
Vol 05 (02) ◽  
pp. 229-256 ◽  
Author(s):  
A. BANDINI ◽  
I. LONGHI
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Galois Extension ◽  
Function Field ◽  
Function Fields ◽  
Global Field ◽  
Selmer Groups ◽  
Characteristic P ◽  
Main Conjecture ◽  
Fitting Ideal

Let F be a global field of characteristic p > 0, 𝔽/F a Galois extension with [Formula: see text] and E/F a non-isotrivial elliptic curve. We study the behavior of Selmer groups SelE(L)l (l any prime) as L varies through the subextensions of 𝔽 via appropriate versions of Mazur's Control Theorem. In the case l = p, we let 𝔽 = ∪ 𝔽d where 𝔽d/F is a [Formula: see text]-extension. We prove that Sel E(𝔽d)p is a cofinitely generated ℤp[[ Gal (ℤd/F)]]-module and we associate to its Pontrjagin dual a Fitting ideal. This allows to define an algebraic L-function associated to E in ℤp[[Gal(ℤ/F)]], providing an ingredient for a function field analogue of Iwasawa's Main Conjecture for elliptic curves.

scholarly journals Counterexamples to Hochschild-Kostant-Rosenberg in characteristic p

2021 ◽  
Vol 9 ◽  
Author(s):  
Benjamin Antieau ◽  
Bhargav Bhatt ◽  
Akhil Mathew
Keyword(s):  
Spectral Sequence ◽  
Spectral Sequences ◽  
Characteristic P ◽  
De Rham

Abstract We give counterexamples to the degeneration of the Hochschild-Kostant-Rosenberg spectral sequence in characteristic p, both in the untwisted and twisted settings. We also prove that the de Rham-HP and crystalline-TP spectral sequences need not degenerate.

Effect of oxygen vacancies and crystal symmetry on piezocatalytic properties of Bi2WO6 ferroelectric nanosheets for wastewater decontamination

2021 ◽  
Author(s):  
Zihan Kang ◽  
Enzhu Lin ◽  
Ni Qin ◽  
Jiang Wu ◽  
Baowei Yuan ◽  
...  
Keyword(s):  
Organic Pollutants ◽  
Oxygen Vacancies ◽  
Mechanical Energy ◽  
Crystal Symmetry ◽  
Characteristic P ◽  
Novel Technique ◽  
Effect Of Oxygen

Piezocatalysis emerged as a novel technique to make use of mechanical energy in dealing with organic pollutants in wastewater. In this work, the ferroelectric Bi2WO6 (BWO) nanosheets with a characteristic...

scholarly journals Synaptic Molecular and Neurophysiological Markers Are Independent Predictors of Progression in Alzheimer’s Disease

2021 ◽  
pp. 1-12
Author(s):  
Una Smailovic ◽  
Ingemar Kåreholt ◽  
Thomas Koenig ◽  
Nicholas J. Ashton ◽  
Bengt Winblad ◽  
...  
Keyword(s):  
Alzheimer’S Disease ◽  
Alzheimer's Disease ◽  
Global Field ◽  
Prognostic Indicators ◽  
Early Event ◽  
Functional Markers ◽  
Beta Band ◽  
Global Field Power ◽  
Synaptic Markers ◽  
Eeg Recordings

Background: Cerebrospinal fluid (CSF) neurogranin and quantitative electroencephalography (qEEG) are potential molecular and functional markers of synaptic pathology in Alzheimer’s disease (AD). Synaptic markers have emerged as candidate prognostic indicators of AD since synaptic degeneration was shown to be an early event and the best correlate of cognitive deficits in patients along the disease continuum. Objective: The present study investigated the association between CSF neurogranin and qEEG measures as well as their potential to predict clinical deterioration in mild cognitive impairment (MCI) patients. Methods: Patients diagnosed with MCI (n = 99) underwent CSF conventional AD biomarkers and neurogranin analysis and resting-state EEG recordings. The study population was further stratified into stable (n = 41) and progressive MCI (n = 31), based on the progression to AD dementia during two years follow-up. qEEG analysis included computation of global field power and global field synchronization in four conventional frequency bands. Results: CSF neurogranin levels were associated with theta power and synchronization in the progressive MCI group. CSF neurogranin and qEEG measures were significant predictors of progression to AD dementia, independent of baseline amyloid status in MCI patients. A combination of CSF neurogranin with global EEG power in theta and global EEG synchronization in beta band exhibited the highest classification accuracy as compared to either of these markers alone. Conclusion: qEEG and CSF neurogranin are independent predictors of progression to AD dementia in MCI patients. Molecular and neurophysiological synaptic markers may have additive value in a multimodal diagnostic and prognostic approach to dementia.

Between interpretation and the subject: Revisiting Bakhtin’s theory of polyphony

Semiotica ◽  
2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jie Zhang ◽  
Hongbing Yu
Keyword(s):  
Literary Theory ◽  
Global Field ◽  
Availability Bias ◽  
Obvious Consequence ◽  
The Subject ◽  
Influential Theory

AbstractThis paper affords a critical and historical reappraisal of Bakhtin’s theory of polyphony. It addresses the issue of the subjectivity of interpretation in the reception and formulation of this highly influential theory in literary semiotics. Following a revaluation of three major patterns of interpretation of polyphony that have emerged in the global field of literary theory since 1929, as well as Bakhtin’s shift in emphasis in 1963, we find that Bakhtin’s theorizing of polyphony, based on his seemingly inconsistent interpretation of Dostoevsky’s novels, was defined by his own subjectivity as well. An obvious consequence of such subjective predispositions in both the reception of Bakhtin’s theory and his own treatment of Dostoevsky’s polyphonic novels is that they have instigated a type of perpetuating availability bias in approaching the theory of polyphony. This revelation is key to understanding the wholeness of the theory of polyphony from a diachronic perspective. By tracing the cultural and intellectual sources of Dostoevsky’s polyphonic creation, this paper attempts to reframe and restore the Bakhtinian idea of polyphony to its fullness, which we believe can be encapsulated in one phrase: harmony without uniformity.

Grit as a Key Factor in the Ability of Students to Achieve Productive Global Field Research

2021 ◽  
Author(s):  
Lindsey J. Mattick ◽  
Breanne E. Lott ◽  
Christina E. Baum ◽  
Amr S. Soliman
Keyword(s):  
Field Research ◽  
Global Field ◽  
Key Factor

scholarly journals SUBALGEBRAS OF THE POLYNOMIAL ALGEBRA IN POSITIVE CHARACTERISTIC AND THE JACOBIAN

2011 ◽  
Vol 10 (04) ◽  
pp. 605-613
Author(s):  
ALEXEY V. GAVRILOV
Keyword(s):  
Principal Ideal ◽  
Positive Characteristic ◽  
Polynomial Algebra ◽  
Characteristic P ◽  
The Ideal

Let 𝕜 be a field of characteristic p > 0 and R be a subalgebra of 𝕜[X] = 𝕜[x1, …, xn]. Let J(R) be the ideal in 𝕜[X] defined by [Formula: see text]. It is shown that if it is a principal ideal then [Formula: see text], where q = pn(p - 1)/2.

THE RAMIFICATION GROUPS AND DIFFERENT OF A COMPOSITUM OF ARTIN–SCHREIER EXTENSIONS

2010 ◽  
Vol 06 (07) ◽  
pp. 1541-1564 ◽  
Author(s):  
QINGQUAN WU ◽  
RENATE SCHEIDLER
Keyword(s):  
Class Number ◽  
Function Field ◽  
Positive Characteristic ◽  
Field Extension ◽  
Constant Field ◽  
Divisor Class ◽  
Characteristic P ◽  
Similar Nature ◽  
Field Of Positive Characteristic ◽  
The Ideal

Let K be a function field over a perfect constant field of positive characteristic p, and L the compositum of n (degree p) Artin–Schreier extensions of K. Then much of the behavior of the degree pn extension L/K is determined by the behavior of the degree p intermediate extensions M/K. For example, we prove that a place of K totally ramifies/is inert/splits completely in L if and only if it totally ramifies/is inert/splits completely in every M. Examples are provided to show that all possible decompositions are in fact possible; in particular, a place can be inert in a non-cyclic Galois function field extension, which is impossible in the case of a number field. Moreover, we give an explicit closed form description of all the different exponents in L/K in terms of those in all the M/K. Results of a similar nature are given for the genus, the regulator, the ideal class number and the divisor class number. In addition, for the case n = 2, we provide an explicit description of the ramification group filtration of L/K.

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