Cohomology of algebraic varieties over the maximal cyclotomic extension of a global field

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

10.23943/princeton/9780691160504.001.0001 ◽

2017 ◽

Author(s):

Claire Voisin

Keyword(s):

Recent Work ◽

Chow Groups ◽

Ring Structure ◽

Complete Intersections ◽

Algebraic Varieties ◽

Chow Ring ◽

Hodge Structures ◽

Chow Rings ◽

Geometric Methods ◽

The Right

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. The book is intended for both students and researchers, and not only presents a survey of the geometric methods developed in the last thirty years to understand the famous Bloch-Beilinson conjectures, but also examines recent work by the author. It focuses on two central objects: the diagonal of a variety—and the partial Bloch-Srinivas type decompositions it may have depending on the size of Chow groups—as well as its small diagonal, which is the right object to consider in order to understand the ring structure on Chow groups and cohomology. An exploration of a sampling of recent works by the author looks at the relation, conjectured in general by Bloch and Beilinson, between the coniveau of general complete intersections and their Chow groups and a very particular property satisfied by the Chow ring of K3 surfaces and conjecturally by hyper-Kähler manifolds. In particular, the book delves into arguments originating in Nori's work that have been further developed by others.

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ALGEBRAIC VARIETIES OVER FIELDS WITH DIFFERENTIATION

Mathematics of the USSR-Sbornik ◽

10.1070/sm1969v009n03abeh002054 ◽

1969 ◽

Vol 9 (3) ◽

pp. 389-413

Author(s):

Ju R Vaĭnberg

Keyword(s):

Algebraic Varieties

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

Journal of Alzheimer s Disease ◽

10.3233/jad-201234 ◽

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.

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

Semiotica ◽

10.1515/sem-2019-0086 ◽

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.

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