The generic isogeny decomposition of the Prym Variety of a cyclic branched covering

Let $$f:S'\longrightarrow S$$ f : S ′ ⟶ S be a cyclic branched covering of smooth projective surfaces over $${\mathbb {C}}$$ C whose branch locus $$\Delta \subset S$$ Δ ⊂ S is a smooth ample divisor. Pick a very ample complete linear system $$|{\mathcal {H}}|$$ | H | on S, such that the polarized surface $$(S, |{\mathcal {H}}|)$$ ( S , | H | ) is not a scroll nor has rational hyperplane sections. For the general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | consider the $$\mu _{n}$$ μ n -equivariant isogeny decomposition of the Prym variety $${{\,\mathrm{Prym}\,}}(C'/C)$$ Prym ( C ′ / C ) of the induced covering $$f:C'{:}{=}f^{-1}(C)\longrightarrow C$$ f : C ′ : = f - 1 ( C ) ⟶ C : $$\begin{aligned} {{\,\mathrm{Prym}\,}}(C'/C)\sim \prod _{d|n,\ d\ne 1}{\mathcal {P}}_{d}(C'/C). \end{aligned}$$ Prym ( C ′ / C ) ∼ ∏ d | n , d ≠ 1 P d ( C ′ / C ) . We show that for the very general member $$[C]\in |{\mathcal {H}}|$$ [ C ] ∈ | H | the isogeny component $${\mathcal {P}}_{d}(C'/C)$$ P d ( C ′ / C ) is $$\mu _{d}$$ μ d -simple with $${{\,\mathrm{End}\,}}_{\mu _{d}}({\mathcal {P}}_{d}(C'/C))\cong {\mathbb {Z}}[\zeta _{d}]$$ End μ d ( P d ( C ′ / C ) ) ≅ Z [ ζ d ] . In addition, for the non-ample case we reformulate the result by considering the identity component of the kernel of the map $${\mathcal {P}}_{d}(C'/C)\subset {{\,\mathrm{Jac}\,}}(C')\longrightarrow {{\,\mathrm{Alb}\,}}(S')$$ P d ( C ′ / C ) ⊂ Jac ( C ′ ) ⟶ Alb ( S ′ ) .

Minimal mindreaders let spinning dogs lie: New evidence for the dual-process account of human mindreading

<p>Five experiments investigated evidence for a dual-process account of mindreading (Apperly, 2010). This account is motivated by two puzzles: First, why is it that three-year-olds fail standard false-belief tests when looking patterns infer that infants are sensitive to others’ false beliefs? Secondly, why is adult mindreading sometimes slow and effortful, and at other times fast and effortless? The seemingly contradictory observations may be explained by drawing upon two relatively distinct mindreading abilities: ‘Efficient’ processing supports precocious infant performances in non-verbal tasks and fast-paced social interaction in adults, while the later developing ‘flexible’ processing permits full blown understanding of beliefs and facilitates correct verbal responding in standard false-belief tests. Evidence for this theory can be sought by exploiting the idea that there are ‘signature limits’ to the type of information that can be efficiently processed. One conjecture is that representations underpinning efficient belief-tracking relate agents to objects, leading to the prediction that efficient processing cannot handle false-beliefs involving identity. Experiments 1 and 2 used a novel action-prediction paradigm to determine if adults’ reaction-time patterns differed between two false-belief tasks, one involving a standard change-of-location scenario, and one which also incorporated an identity component. The findings revealed equivalent flexible processing across both tasks. However, there were distinct reaction-time profiles between the tasks such that efficient belief-tracking was only observed in the change-of-location task. The absence of efficient processing in the task incorporating an identity component supports the conjecture that efficient belief-tracking is limited to relational, rather than propositional attitudes. A second conjecture is that representations underpinning efficient belief-tracking either do not specify agents’ locations or do not specify objects’ orientations. This leads to the prediction that efficient belief-tracking alone will not yield expectations about agents’ perspectives. In a novel object-detection paradigm, Experiments 3 to 5 tested the extent to which adults efficiently tracked the belief of a passive bystander in two closely-matched but conceptually distinct tasks. In a task involving homogenous objects, reaction times were involuntarily influenced by the presence of the bystander. By contrast, in a second task in which the object could be differently perceived depending on where the agent was located in relation to that object, the presence of the agent did not influence adults’ response times, supporting the second conjecture.</p>

Minimal mindreaders let spinning dogs lie: New evidence for the dual-process account of human mindreading

<p>Five experiments investigated evidence for a dual-process account of mindreading (Apperly, 2010). This account is motivated by two puzzles: First, why is it that three-year-olds fail standard false-belief tests when looking patterns infer that infants are sensitive to others’ false beliefs? Secondly, why is adult mindreading sometimes slow and effortful, and at other times fast and effortless? The seemingly contradictory observations may be explained by drawing upon two relatively distinct mindreading abilities: ‘Efficient’ processing supports precocious infant performances in non-verbal tasks and fast-paced social interaction in adults, while the later developing ‘flexible’ processing permits full blown understanding of beliefs and facilitates correct verbal responding in standard false-belief tests. Evidence for this theory can be sought by exploiting the idea that there are ‘signature limits’ to the type of information that can be efficiently processed. One conjecture is that representations underpinning efficient belief-tracking relate agents to objects, leading to the prediction that efficient processing cannot handle false-beliefs involving identity. Experiments 1 and 2 used a novel action-prediction paradigm to determine if adults’ reaction-time patterns differed between two false-belief tasks, one involving a standard change-of-location scenario, and one which also incorporated an identity component. The findings revealed equivalent flexible processing across both tasks. However, there were distinct reaction-time profiles between the tasks such that efficient belief-tracking was only observed in the change-of-location task. The absence of efficient processing in the task incorporating an identity component supports the conjecture that efficient belief-tracking is limited to relational, rather than propositional attitudes. A second conjecture is that representations underpinning efficient belief-tracking either do not specify agents’ locations or do not specify objects’ orientations. This leads to the prediction that efficient belief-tracking alone will not yield expectations about agents’ perspectives. In a novel object-detection paradigm, Experiments 3 to 5 tested the extent to which adults efficiently tracked the belief of a passive bystander in two closely-matched but conceptually distinct tasks. In a task involving homogenous objects, reaction times were involuntarily influenced by the presence of the bystander. By contrast, in a second task in which the object could be differently perceived depending on where the agent was located in relation to that object, the presence of the agent did not influence adults’ response times, supporting the second conjecture.</p>

Development of Personal Identity Among Sami Adolescents Living in the Arctic Territories of Russia

The article is devoted to the problem of studying the personal identity of Sami adolescents living in the Arctic territories of Russia. The study aims to study the characteristics of the personal identity of Sami boys and Sami girls in adolescence. The article presents the results of an empirical study carried out according to the methodology developed based on the test “Who am I?” developed by Kuhn and McPartland. The respondents were 39 Sami adolescents aged 12-13 years and 40 Sami adolescents aged 14-15 years. All respondents were from the indigenous Sami people. When studying personal identity, we analyzed the characteristics corresponding to each identity component: gender, social, ethnic, family, professional, individual, physical, active and undifferentiated. The study results made it possible to reveal the characteristics of the personal identity of Sami adolescents compared to the personal identity of their Russian peers. The data obtained expand modern psychological ideas about the patterns of personality development in adolescence, how the human psyche functions in a changing world, and clarify the meaningful characteristics of the psychological portrait of a modern adolescent.

COMMUTING PROBABILITY OF COMPACT GROUPS

For any (Hausdorff) compact group G, denote by $\mathrm{cp}(G)$ the probability that a randomly chosen pair of elements of G commute. We prove that there exists a finite group H such that $\mathrm{cp}(G)= {\mathrm{cp}(H)}/{|G:F|^2}$ , where F is the FC-centre of G and H is isoclinic to F with $\mathrm{cp}(F)=\mathrm{cp}(H)$ whenever $\mathrm{cp}(G)>0$ . In addition, we prove that a compact group G with $\mathrm{cp}(G)>\tfrac {3}{40}$ is either solvable or isomorphic to $A_5 \times Z(G)$ , where $A_5$ denotes the alternating group of degree five and the centre $Z(G)$ of G contains the identity component of G.

Complete reducibility: variations on a theme of Serre

In this note, we unify and extend various concepts in the area of G-complete reducibility, where G is a reductive algebraic group. By results of Serre and Bate–Martin–Röhrle, the usual notion of G-complete reducibility can be re-framed as a property of an action of a group on the spherical building of the identity component of G. We show that other variations of this notion, such as relative complete reducibility and $$\sigma $$ σ -complete reducibility, can also be viewed as special cases of this building-theoretic definition, and hence a number of results from these areas are special cases of more general properties.

Towards the Sato–Tate groups of trinomial hyperelliptic curves

We consider the identity component of the Sato–Tate group of the Jacobian of curves of the form [Formula: see text] where [Formula: see text] is the genus of the curve and [Formula: see text] is constant. We approach this problem in three ways. First we use a theorem of Kani-Rosen to determine the splitting of Jacobians for [Formula: see text] curves of genus 4 and 5 and prove what the identity component of the Sato–Tate group is in each case. We then determine the splitting of Jacobians of higher genus [Formula: see text] curves by finding maps to lower genus curves and then computing pullbacks of differential 1-forms. In using this method, we are able to relate the Jacobians of curves of the form [Formula: see text], [Formula: see text] and [Formula: see text]. Finally, we develop a new method for computing the identity component of the Sato–Tate groups of the Jacobians of the three families of curves. We use this method to compute many explicit examples, and find surprising patterns in the shapes of the identity components [Formula: see text] for these families of curves.

A Note on Invariant Basis Number and Types for Strongly Graded Rings

: Given any pair of positive integers (n, k) and any nontrivial finite group G, we show that there exists a ring R of type (n, k) such that R is strongly graded by G and the identity component Re has Invariant Basis Number. Moreover, for another pair of positive integers (n', k') with n ≤ n' and k | k', it is proved that there exists a ring R of type (n, k) such that R is strongly graded by G and Re has type (n', k'). These results were mentioned in [G. Abrams, Invariant basis number and types for strongly graded rings, J. Algebra 237 (2001) 32-37] without proofs.

The Manifestation of the Psychologist's Professional Identity in the Characteristics of the Communicative and Gendered 'Me'

This article represents an analysis of professional identity of the psychologist in conjunction with with the features of their communicative and gender ‘Me’. The work of the psychologist is seen in different systems: person-person, person-group, person-society. Difficulties associated with the need to build quality person-centred communication, but at the same time maintain the boundaries of professional care, are described. In this case, communication competence can be considered not only as criterion of rendering efficient help to a client, but as a condition for forming professional identity of the psychologist. This paper presents the results of an empirical study of the identity of psychologists using the techniques of T. Kun, T. McPartland ‘Who am I’ (in versions by T.V. Rumyantseva, I. S. Kletsina, N.L. Ivanova). The processing of the results included quantitative and qualitative analysis. The analysis of the data revealed the components of identity that may hinder the formation of a stable professional identity. It has been shown that psychologists are primarily oriented towards constructing identity through personal dispositions; the communicative component of their identity is linked to their professional image. A poorly expressed necessity in communication, or domination of negative characteristics in describing one’s own communication skills is reflected in the psychologist’s lack of professional identity. When a professional identity is formed, the aspects of gender identity become blurred and professional characteristics that are the professionally important qualities of psychologists begin to dominate in personality descriptions. The connection between the formation of the psychologist’s professional identity and the peculiarities of their communicative and gendered ‘Me’ is shown. The individual’s acceptance of professionally important qualities (as a positively formed communicative identity component and gender-neutral characteristics) allows the psychologist to build a sustainable positive professional identity.