Examples Of Motives Research Articles

Relative Equivariant Motives and Modules

AbstractWe introduce and study various categories of (equivariant) motives of (versal) flag varieties. We relate these categories with certain categories of parabolic (Demazure) modules. We show that the motivic decomposition type of a versal flag variety depends on the direct sum decomposition type of the parabolic module. To do this we use localization techniques of Kostant and Kumar in the context of generalized oriented cohomology as well as the Rost nilpotence principle for algebraic cobordism and its generic version. As an application, we obtain new proofs and examples of indecomposable Chow motives of versal flag varieties.

Automorphy and irreducibility of some l-adic representations

AbstractIn this paper we prove that a pure, regular, totally odd, polarizable weakly compatible system of $l$-adic representations is potentially automorphic. The innovation is that we make no irreducibility assumption, but we make a purity assumption instead. For compatible systems coming from geometry, purity is often easier to check than irreducibility. We use Katz’s theory of rigid local systems to construct many examples of motives to which our theorem applies. We also show that if $F$ is a CM or totally real field and if ${\it\pi}$ is a polarizable, regular algebraic, cuspidal automorphic representation of $\text{GL}_{n}(\mathbb{A}_{F})$, then for a positive Dirichlet density set of rational primes $l$, the $l$-adic representations $r_{l,\imath }({\it\pi})$ associated to ${\it\pi}$ are irreducible.

Theoretical and Practical Aspects of Volunteer Organisation Members (Volunteers) Motivation

Nowadays non-profit organisations that offer different services are getting more and more recognition. Organisation activities appeal to voluntary work. Presented services are more qualitative because they are fulfilled by dedicated volunteers; they are more efficient, because volunteers are not paid. Sometimes it happens not to know how to initiate the process of organisation development: not every member is involved into the process of voluntary organisation even if he has very good ideas; work is distributed inefficiently etc. Then many members become disappointed in such activity and do not believe that they can change or improve something in their lives. A closed circle forms: there are people who wish to work for the good of community but poor work motivation and misjudgement of initiatives disappoint people, and social activity sort of “dies” or is performed by two or three the most active members. Therefore such activity becomes more “on paper” than practical. It is very important that as much people as possible would understand the input and importance of their work and could act the country wellbeing and their welfare. Efficient motivation of volunteers work is necessary on purpose to achieve these goals. Behaviour of every person is determined by motives that are inner forces stimulating performance of certain actions. Motives are regulated by human needs realizing possibility and degree of their satisfaction. Human behaviour is pointless if motives and aims of the behaviour were incomprehensible. People motivation is pursuit to satisfy essential needs and to acquire something what is missing. People actualizing themselves do not have unsatisfied fundamental needs but they have impulsions. They work, endeavour and have ambitions, although not in the common meaning. Motivations for such people mean character perfection and expression, maturation and growth, in other words actualization of themselves in voluntary activity. Attitudes towards motivation and motives, motivation means of work activation of volunteer organisation members (volunteers) are analyzed in the publication. Importance of volunteers’ motives to continuity of voluntary work is highlighted; essential examples of voluntary work motives and motivation means are indicated. Benefit and difficulties of proper volunteers’ motivation are explained, possibilities of voluntary work are discussed.DOI: http://dx.doi.org/10.5755/j01.ee.23.5.3132

Motivic splitting lemma

Let M be a Chow motive over a field F . Let X be a smooth projective variety over F and N be a direct summand of the motive of X . Assume that over the generic point of X the motives M and N become isomorphic to a direct sum of twisted Tate motives. The main result of the paper says that if a morphism f: M \to N splits over the generic point of X then it splits over F , i.e., N is a direct summand of M . We apply this result to various examples of motives of projective homogeneous varieties.

How to deal with female circumcision as a health issue in the Nordic countries

Roughly 100 000 immigrants in the Nordic countries originate from areas in Africa where the tradition of FGC is still well known. A majority of this immigrant group consists of Somali women and men (approximately 25 000 in Sweden 16 000 in Denmark 8000 in Norway and 7000 in Finland less than 10 in Iceland; national statistics figures). FGC in the Nordic countries became an issue in the 1980s. The civil war in Somalia caused many Somalis to leave their country in the early 1990s. The arrival of large groups of Somali families forced the Nordic societies to take a stand on the health issue of FGC. Traditionally Somali girls are infibulated which involves excision of the clitoris labia minora and stitching of the vaginal opening. Health providers and social professionals in the Nordic countries are therefore obliged to know how to handle this issue. The primary motives for FGC in Somalia are that the practice is experienced as a religious duty and a prerequisite of marriage. Based on clinical experience the most common reaction to FGC in a Western country is one of disgust and rejection. However in countries where FGC is practiced it is looked upon as the "normal" state sometimes expressed in line with the following citations: "being smooth in the genital area without flaps is a beauty ideal" "if the labia minora are not cut they will continue to grow" "the clitoris and the labia minora have to be concealed in order to reduce sexual desire to reduce the risk of promiscuity promote fertility and make childbirth easier or the girl will not become a woman" "circumcision will ensure that the woman is a virgin as she gets married." These examples of motives do not necessarily coexist in the same ethnic groups. Thus FGC has deep and complex social and cultural roots that we cannot ignore when discussing how to best deal with FGC as a health issue in the Nordic countries. (excerpt)

On motives for Deligne-Mumford stacks

We define and compare two different definitions of Chow motives for Deligne-Mumford stacks, associated with two definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of motives of algebraic varieties, but the motives of a given stack associated with both theories are not isomorphic. We will also give some examples of motives associated with some alegbraic stacks.

Observations on Fermat Motives ofK3-Type

In [8, 9], Zarhin introduced the notion of varieties ofK3-typein even dimension over finite fields. Zarhin showed that ordinary abelian surfaces, ordinaryK3 surfaces, and ordinary cubic fourfolds are examples of such varieties. As Zarhin already points out, it is easy to extend his method to definemotivesofK3-type. In this note, we extend Zarhin's work by giving this definition and then finding and studying a large number of examples of such motives. Our examples are Fermat motives, i.e., they arise from the Fermat varietyX:Xm0+Xm1+…+Xmn+1=0⊂Pnof degreemand dimensionn=2d. Such motives ofK3-type need not be ordinary; on the other hand, they are never supersingular (essentially by definition—see [1], Chapter 3). Hence, ourK3-type motives give rise to transcendental cycles. We show that being ofK3-type is (resp. is not) hereditary with respect to thetype I inductive structure(resp. thetype II inductive structure) of Fermat motives. When the degreemtends to infinity, the type I inductive structure gives rise to infinitely many Fermat motives ofK3-type (see Remark (3.9)). Following a suggestion of Zarhin, we also consider powers of Fermat motives ofK3-type. Powers of motives ofK3-type are no longer ofK3-type, and hence they can give rise to classes of algebraic cycles. Thus, it is of interest to establish the validity of Tate's conjecture for powers of Fermat motives ofK3-type. This is done in the Section 4, extending Theorem (6.1) of Zarhin [10]. Finally, in Section 5 we discuss theBrauer numbersof Fermat motives ofK3-type, especially, of even composite degreem. This is an attempt to extend the results about Brauer numbers of Fermat motives (of prime or odd prime power degree) in Gouvêa and Yui [1, 2], Miki [4], Shoida [5], and Yui [7]. Throughout, we retain Zarhin's assumptions that the dimensionnis even and that we are working over a finite field.

Reasons for Political Involvement: a Study of Contributors To the 1972 Presidential Campaign

SINCE the publication of Clark and Wilson's classic description of the motivations for participation in group activity, much attention has been given to this important area of investigation, and especially to the motives for participation in political organizations (Clark and Wilson 1961; Bowman, Ippolito, and Donaldson 1969; Browder and Ippolito 1972; Burrell 1982; Conway and Fiegert 1974; Defelice, 1981; Hitlin and Jackson 1977; Hofstetter 1971; Ippolito 1969; Nakamura and Sullivan 1981; Salisbury 1965-1966; Soule and Clarke 1970; and Wilson 1973). Clark and Wilson (1961) identified three broad categories of motivation: material, purposive, and solidary (Wilson 1973). Material motives are basically those involving pecuniary gain. The hope of garnering a government contract, getting a job, obtaining discounts on services, and improving in tax circumstances are all examples of material motives. Purposive motives are intangible; they derive from the sense of satisfaction of having contributed to the attainment of a worthwhile cause (Wilson 1973: 34). A desire to help others, to improve the environment, or to end a corrupt practice, each for the benefit of a public larger than oneself, are purposive motives. Solidary motives are fundamentally social motives. Within this broad category of motives are two variants, specific and collective. Specific solidary motives are those which arise out of the act of and which can be given to, or withheld from, specific individuals (Wilson 1973: 33-34). Deference, receiving an honor, and office-holding are typically specific solidary motives. Collective solidary incentives are intangible rewards created by the act of associating that must be enjoyed by a group if they are to be enjoyed by anyone (Wilson 1973: 34). Friendship, fun, and conviviality are examples of collective solidary motives. It should go without saying that the motivations of political activists are critical for our understanding of any modestly responsive political system (Verba and Nie 1972, and Kessel 1980). For example, many students of the motivations of political activists argue that political organization activists begin with a concern for task-oriented civic purposes only to become disillusioned and change their orientations toward the material and solidary dimensions (Elderveld 1964, Conway and Fiegert 1968, and Roback 1980). Verba and Nie argue that the election-oriented modes of