48,117 research outputs found

    Zeta functions of regular arithmetic schemes at s=0

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    Lichtenbaum conjectured the existence of a Weil-\'etale cohomology in order to describe the vanishing order and the special value of the Zeta function of an arithmetic scheme X\mathcal{X} at s=0s=0 in terms of Euler-Poincar\'e characteristics. Assuming the (conjectured) finite generation of some \'etale motivic cohomology groups we construct such a cohomology theory for regular schemes proper over Spec(Z)\mathrm{Spec}(\mathbb{Z}). In particular, we obtain (unconditionally) the right Weil-\'etale cohomology for geometrically cellular schemes over number rings. We state a conjecture expressing the vanishing order and the special value up to sign of the Zeta function ζ(X,s)\zeta(\mathcal{X},s) at s=0s=0 in terms of a perfect complex of abelian groups RΓW,c(X,Z)R\Gamma_{W,c}(\mathcal{X},\mathbb{Z}). Then we relate this conjecture to Soul\'e's conjecture and to the Tamagawa number conjecture of Bloch-Kato, and deduce its validity in simple cases.Comment: 53 pages. To appear in Duke Math.

    Let's face it. A review of Keenan, Gallup, & Falk's book "The Face in the Mirror"

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    Using neuroimaging experiments and neuropsychological case studies, Keenan mainly examines the neural basis of mirror self-recognition (MSR) and Theory of Mind (TOM), and proposes that self-awareness is dominantly associated with areas of the right hemisphere. I believe that this conclusion is both inflated and premature. MSR is only superficially related to genuine, fully mature human self-awareness. Furthermore, TOM should not be equated with self-awareness because some forms of it (e.g., self-rumination) actually interfere with thinking about others' mental states. One more general (and serious) problem with the book is the proposal that because MSR and TOM are mainly generated by right hemispheric activity, then it follows that self-awareness itself is associated with activity of the same hemisphere. Recent studies on autobiographical memory and self-description also indicate left hemispheric activit

    On the importance of inner speech for self-awareness

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    In this presentation I use recent empirical evidence and theoretical analyses concerning the importance of language in consciousness. Preliminary clinical and neuropsychological data indicate that inner speech is deeply linked to self-awareness; also, four hypotheses concerning the crucial role inner speech plays in self-focus are presented. I conclude by proposing that genuine consciousness (i.e., self-awareness) is impossible without language

    The Weil-\'etale fundamental group of a number field I

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    Lichtenbaum has conjectured the existence of a Grothendieck topology for an arithmetic scheme XX such that the Euler characteristic of the cohomology groups of the constant sheaf Z\mathbb{Z} with compact support at infinity gives, up to sign, the leading term of the zeta-function ζX(s)\zeta_X(s) at s=0s=0. In this paper we consider the category of sheaves XˉL\bar{X}_L on this conjectural site for X=Spec(OF)X=Spec(\mathcal{O}_F) the spectrum of a number ring. We show that XˉL\bar{X}_L has, under natural topological assumptions, a well defined fundamental group whose abelianization is isomorphic, as a topological group, to the Arakelov Picard group of FF. This leads us to give a list of topological properties that should be satisfied by XˉL\bar{X}_L. These properties can be seen as a global version of the axioms for the Weil group. Finally, we show that any topos satisfying these properties gives rise to complexes of \'etale sheaves computing the expected Lichtenbaum cohomology.Comment: 40 pages. To appear in Kyushu Journal of Mathematic

    America's Four Middle Classes

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    Presents survey findings on the attitudes, outlook, and financial status of four groups among the middle class -- top-of-the-class, satisfied, anxious, and struggling -- and each group's composition by demographics, education, and income

    Self-awareness review Part 1: Do you “self-reflect” or “self-ruminate”?

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    We all spend time analyzing our inner thoughts and feelings; past research looked at this activity as being unitary in nature (i.e., simply focusing on the self), examined how frequently people introspect, and identified the effects of self-focus on behavior. Current studies indicate that people actually engage in two different types of self-analysis: self-reflection (enjoying analyzing the self) and self-rumination (not being able to shut off thoughts about the self), each leading to opposite consequences

    Right hemispheric self-awareness: A critical assessment

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    In this commentaryI evaluate the claim made byKeenan, Nelson, OConnor, and Pascual-Leone (2001) that since self-recognition results from right hemispheric activity, self-awareness too is likely to be produced by the activity of the same hemisphere. This reasoning is based on the assumption that self-recognition represents a valid operationalization of self-awareness; I present two views that challenge this rationale. Keenan et al. also support their claim with published evidence relating brain activityand self-awareness; I closely examine their analysis of one specific review of literature and conclude that it appears to be biased. Finally, recent research suggests that inner speech (which is associated with left hemispheric activity) is linked to self-awareness—an observation that further casts doubt on the existence of a right hemispheric self-awareness

    Self-awareness, self-recognition, and Theory of Mind: Conceptual distinctions and neuroanatomic localization

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    Comment on Keenan's (2003) hypothesis that self-recognition, Theory-of-Mind, and self-awareness are located in the right hemispher

    Restricted Complexity, General Complexity

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    Why has the problematic of complexity appeared so late? And why would it be justified

    The Late Works of Dame Ethel Smyth: A Musical Microcosm of Interwar British Culture

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    This paper examines the late musical compositions of Dame Ethel Smyth in the context of British society and culture between the two World Wars. It focuses on Smyth\u27s large-scale works, especially her operas The Boatswain\u27s Mate (1914) and Entente Cordiale (1923-1924) and her oratorio The Prison (1930). Using these works as examples of the composer\u27s mature style, I draw attention to a number of Smyth\u27s original artistic choices as well as her sophisticated use of social commentary. Also considered in this research are certain anticipated roles for women as composers at the time, Smyth\u27s other passions and pursuits, and her interactions with her contemporaries. Her activities as a composer reflected an evolving social landscape for British women in addition to new musical developments
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