scholarly journals The Fields of Moduli for Polarized Abelian Varieties and for Curves

1972 ◽  
Vol 48 ◽  
pp. 37-55 ◽  
Author(s):  
Shoji Koizumi
Keyword(s):  
Algebraic Geometry ◽  
Characteristic Zero ◽  
Essential Role ◽  
Positive Characteristic ◽  
Abelian Varieties ◽  
Complex Multiplications ◽  
Definition Of ◽  
Fields Of Moduli

In the study of moduli of polarized abelian varieties and of curves as well as in the theory of complex multiplications, the notion of fields of moduli for structures plays an essential role. This notion was first introduced by Matsusaka [7] for polarized varieties with some pleasing properties and later was given a more comprehensible treatment by Shimura [10] in the case of polarized abelian varieties or polarized abelian varieties with some further structures. Both authors discussed fields of moduli not only in algebraic geometry of characteristic zero but also in that of positive characteristic, but in the latter case the definition of fields of moduli seems somewhat artificial and there have been no essential applications of them so far.

scholarly journals Questions de corps de définition pour les variétés abéliennes en caractéristique positive

2008 ◽  
Vol 7 (4) ◽  
pp. 623-639 ◽  
Author(s):  
Franck Benoist ◽  
Françoise Delon
Keyword(s):  
Algebraic Geometry ◽  
Abelian Variety ◽  
Positive Characteristic ◽  
Abelian Varieties ◽  
Direct Proof ◽  
Point Of View ◽  
Theoretical Point ◽  
Definition Of

AbstractDichotomies in various conjectures from algebraic geometry are in fact occurrences of the dichotomy among Zariski structures. This is what Hrushovski showed and which enabled him to solve, positively, the geometric Mordell–Lang conjecture in positive characteristic. Are we able now to avoid this use of Zariski structures? Pillay and Ziegler have given a direct proof that works for semi-abelian varieties they called ‘very thin’, which include the ordinary abelian varieties. But it does not apply in all generality: we describe here an abelian variety which is not very thin. More generally, we consider from a model-theoretical point of view several questions about the fields of definition of semi-abelian varieties.

scholarly journals Fibrations with moving cuspidal singularities

1991 ◽  
Vol 122 ◽  
pp. 161-179 ◽  
Author(s):  
Yoshifumi Takeda
Keyword(s):  
Algebraic Geometry ◽  
Characteristic Zero ◽  
Positive Characteristic ◽  
Closed Field ◽  
Projective Surface ◽  
Projective Curve ◽  
Smooth Projective Curve ◽  
Algebraically Closed Field ◽  
Smooth Projective Surface ◽  
Almost All

Let f: V → C be a fibration from a smooth projective surface onto a smooth projective curve over an algebraically closed field k. In the case of characteristic zero, almost all fibres of f are nonsingular. In the case of positive characteristic, it is, however, known that there exist fibrations whose general fibres have singularities. Moreover, it seems that such fibrations often have pathological phenomena of algebraic geometry in positive characteristic (see M. Raynaud [7], W. Lang [4]).

scholarly journals Erratum to: Fields of moduli and definition of hyperelliptic covers

2013 ◽  
Vol 101 (6) ◽  
pp. 599-600
Author(s):  
Yolanda Fuertes ◽  
Gabino González-Diez
Keyword(s):  
Definition Of ◽  
Fields Of Moduli

ON THE RANK OF ABELIAN VARIETIES OVER AMPLE FIELDS

2010 ◽  
Vol 06 (03) ◽  
pp. 579-586 ◽  
Author(s):  
ARNO FEHM ◽  
SEBASTIAN PETERSEN
Keyword(s):  
Finite Field ◽  
Abelian Variety ◽  
Galois Extension ◽  
Characteristic Zero ◽  
Rational Point ◽  
Abelian Varieties ◽  
Finitely Generated ◽  
Infinite Rank ◽  
Finite Set

A field K is called ample if every smooth K-curve that has a K-rational point has infinitely many of them. We prove two theorems to support the following conjecture, which is inspired by classical infinite rank results: Every non-zero Abelian variety A over an ample field K which is not algebraic over a finite field has infinite rank. First, the ℤ(p)-module A(K) ⊗ ℤ(p) is not finitely generated, where p is the characteristic of K. In particular, the conjecture holds for fields of characteristic zero. Second, if K is an infinite finitely generated field and S is a finite set of local primes of K, then every Abelian variety over K acquires infinite rank over certain subfields of the maximal totally S-adic Galois extension of K. This strengthens a recent infinite rank result of Geyer and Jarden.

scholarly journals The Politics of Peoplehood

2015 ◽  
Vol 45 (4) ◽  
pp. 439-465 ◽  
Author(s):  
Jonathan White ◽  
Lea Ypi
Keyword(s):  
Political Theory ◽  
Essential Role ◽  
Political Legitimacy ◽  
Political Conflict ◽  
The People ◽  
Definition Of

Contemporary political theory has made the question of the “people” a topic of sustained analysis. This article identifies two broad approaches taken—norm-based and contestation-based—and, noting some problems left outstanding, goes on to advance a complementary account centred on partisan practice. It suggests the definition of “the people” is closely bound up in the analysis of political conflict, and that partisans engaged in such conflict play an essential role in constructing and contesting different principled conceptions. The article goes on to show how such an account does not lead to a normatively hollow, purely historical conception of “the people,” but rather highlights the normative importance of practices that, at the minimum, de-naturalise undesirable conceptions of the people and, at their best, give political legitimacy and a representative basis to those one might wish to see prosper.

ʿAdālat al-Ṣaḥāba: The Construction of a Religious Doctrine

Arabica ◽  
2013 ◽  
Vol 60 (3-4) ◽  
pp. 272-305 ◽  
Author(s):  
Amr Osman
Keyword(s):  
Civil Wars ◽  
Essential Role ◽  
Conclusive Evidence ◽  
Presumption Of Innocence ◽  
Textual Evidence ◽  
Religious Doctrine ◽  
Definition Of

Abstract This article investigates the development of ʿadālat al-ṣaḥāba, a central doctrine in Sunnī orthodoxy that stresses the integrity of the Prophet Muḥammad’s Companions. The examination of relevant Sunnī works indicates that the doctrine crystalized in the 5th/11th century, by which time the basic tenets of the doctrine had been developed. These include, among other things, the definition of Companions and their essential role in securing the authenticity of Islam. Furthermore, it was around that time that medieval Sunnī scholars developed an epistemological—rather than a historical or theological—basis for the doctrine. Establishing the integrity of the Companions during the Prophet’s lifetime on the presumption of innocence that is further confirmed by textual evidence, they argued that good Muslims must continue to accept that integrity given the lack of conclusive evidence that they lost it at a later time, particularly when they participated in civil wars. I argue that this epistemological ground was furnished by Murğiʾism, as the examination of some Murğiʾī texts demonstrates.1

scholarly journals Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

2008 ◽  
Vol 191 ◽  
pp. 111-134 ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Characteristic Zero ◽  
General Type ◽  
Positive Characteristic ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Arbitrary Characteristic ◽  
Numerical Invariants ◽  
Characteristic 2

AbstractWe establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

scholarly journals The essential role of law in achieving the health-related Sustainable Development Goals

2020 ◽  
Vol 30 (Supplement_1) ◽  
pp. i32-i35
Author(s):  
Dineke Zeegers Paget ◽  
David Patterson
Keyword(s):  
Sustainable Development ◽  
Essential Role ◽  
Sustainable Development Goals ◽  
World Health ◽  
International Human Rights Law ◽  
Health Related ◽  
Development Goals ◽  
Definition Of ◽  
The Right

Abstract In this article, we examine the essential role of law in achieving the health-related Sustainable Development Goals (SDGs). Following the World Health Organization’s broad definition of health, all SDGs can be seen to impact on human health and hence the health goal (SDG3) should be right at the centre of the entire 2030 Agenda for Sustainable Development. We note recent research on the contribution of law, including international human rights law, to achieving health for all and discuss the role of law in addressing seven emerging health challenges. Law can and should play an important role in achieving all health-related SDGs, by respecting, protecting and fulfilling the right to health, ensuring that no one is left behind.

ARISTOPHANES VS TYPHON: CO(S)MIC RIVALRY, VOICE AND TEMPORALITY INKNIGHTS

Ramus ◽  
2014 ◽  
Vol 43 (1) ◽  
pp. 25-44 ◽  
Author(s):  
Mario Telò
Keyword(s):  
Essential Role ◽  
Fifth Century ◽  
Political Factions ◽  
Dramatic Performance ◽  
Definition Of ◽  
Somatic Experiences

Recent studies have analysed the essential role of interpoetic rivalry in Aristophanes' comic imagination. Zachary Biles has shown that ‘festival agonistics provide an underlying logic for the overall thematic design of individual plays’ and that ‘the plays can be treated as creative responses to the competitions.’ Aristophanes' dramatisation of comic competition has been viewed as a reflection of the struggles of political factions in late-fifth-century Athens or as an expression of a ‘rhetoric of self-promotion’ that builds the comic plot through the mutual borrowing of comic material (jokes, running gags). This paper suggests thatKnightspresents interpoetic rivalry as a conflict of embodied aesthetic modes. In this play, Aristophanes' tendentious definition of his comic self against his predecessor Cratinus results in opposed ways of conceptualising the sonic quality of dramatic performance and its material effects on the audience. The nexus of voice and temporality, which, as I argue, shapes the play's agonistic plot, equates the intergenerational duelling of Aristophanes' and Cratinus' political counterparts (the Sausage Seller and the older Paphlagon, respectively) to a contrast of somatic experiences grounded in sound.

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