scholarly journals Picard curves over with good reduction away from 3

2016 ◽  
Vol 19 (2) ◽  
pp. 382-408 ◽  
Author(s):  
Beth Malmskog ◽  
Christopher Rasmussen
Keyword(s):  
Good Reduction ◽  
Binary Forms ◽  
Linear Factor ◽  
Isomorphism Classes ◽  
Picard Curves ◽  
Exhaustive List

Inspired by methods of N. P. Smart, we describe an algorithm to determine all Picard curves over $\mathbb{Q}$ with good reduction away from 3, up to $\mathbb{Q}$-isomorphism. A correspondence between the isomorphism classes of such curves and certain quintic binary forms possessing a rational linear factor is established. An exhaustive list of integral models is determined and an application to a question of Ihara is discussed.

scholarly journals Spinor groups with good reduction

2019 ◽  
Vol 155 (3) ◽  
pp. 484-527 ◽  
Author(s):  
Vladimir I. Chernousov ◽  
Andrei S. Rapinchuk ◽  
Igor A. Rapinchuk
Keyword(s):  
Quadratic Forms ◽  
Galois Cohomology ◽  
Unitary Groups ◽  
Global Field ◽  
Two Dimensional ◽  
Good Reduction ◽  
Isomorphism Classes ◽  
Unramified Cohomology ◽  
Finiteness Properties ◽  
Local Map

Let $K$ be a two-dimensional global field of characteristic $\neq 2$ and let $V$ be a divisorial set of places of $K$. We show that for a given $n\geqslant 5$, the set of $K$-isomorphism classes of spinor groups $G=\operatorname{Spin}_{n}(q)$ of nondegenerate $n$-dimensional quadratic forms over $K$ that have good reduction at all $v\in V$ is finite. This result yields some other finiteness properties, such as the finiteness of the genus $\mathbf{gen}_{K}(G)$ and the properness of the global-to-local map in Galois cohomology. The proof relies on the finiteness of the unramified cohomology groups $H^{i}(K,\unicode[STIX]{x1D707}_{2})_{V}$ for $i\geqslant 1$ established in the paper. The results for spinor groups are then extended to some unitary groups and to groups of type $\mathsf{G}_{2}$.

scholarly journals An inverse Jacobian algorithm for Picard curves

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Joan-C. Lario ◽  
Anna Somoza ◽  
Christelle Vincent
Keyword(s):  
Class Number ◽  
Complex Multiplication ◽  
Hyperelliptic Curves ◽  
Period Matrix ◽  
Isomorphism Classes ◽  
Jacobian Problem ◽  
Picard Curves ◽  
The Given ◽  
Small Period ◽  
Jacobian Algorithm

AbstractWe study the inverse Jacobian problem for the case of Picard curves over $${\mathbb {C}}$$ C . More precisely, we elaborate on an algorithm that, given a small period matrix $$\varOmega \in {\mathbb {C}}^{3\times 3}$$ Ω ∈ C 3 × 3 corresponding to a principally polarized abelian threefold equipped with an automorphism of order 3, returns a Legendre–Rosenhain equation for a Picard curve with Jacobian isomorphic to the given abelian variety. Our method corrects a formula obtained by Koike–Weng (Math Comput 74(249):499–518, 2005) which is based on a theorem of Siegel. As a result, we apply the algorithm to obtain equations of all the isomorphism classes of Picard curves with maximal complex multiplication by the maximal order of the sextic CM-fields with class number at most $$4$$ 4 . In particular, we obtain the complete list of maximal CM Picard curves defined over $${\mathbb {Q}}$$ Q . In the appendix, Vincent gives a correction to the generalization of Takase’s formula for the inverse Jacobian problem for hyperelliptic curves given in [Balakrishnan–Ionica–Lauter–Vincent, LMS J. Comput. Math., 19(suppl. A):283-300, 2016].

scholarly journals Primes Dividing Invariants of CM Picard Curves

2019 ◽  
Vol 72 (2) ◽  
pp. 480-504 ◽  
Author(s):  
Pınar Kılıçer ◽  
Elisa Lorenzo García ◽  
Marco Streng
Keyword(s):  
Complex Multiplication ◽  
Good Reduction ◽  
Explicit Constructions ◽  
Picard Curves ◽  
Genus 2 ◽  
Reduction Of Curves

AbstractWe give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus 3, our bound is sharp enough for use in explicit constructions of Picard curves.

Lessons Learned From Coaching Postsecondary Students With Traumatic Brain Injury

2020 ◽  
Vol 5 (1) ◽  
pp. 88-96
Author(s):  
Mary R. T. Kennedy
Keyword(s):  
College Students ◽  
Traumatic Brain Injury ◽  
Brain Injury ◽  
Sense Of Self ◽  
Scientific Evidence ◽  
Sudden Onset ◽  
Lessons Learned ◽  
Speech Language Pathologists ◽  
The Brain ◽  
Exhaustive List

Purpose The purpose of this clinical focus article is to provide speech-language pathologists with a brief update of the evidence that provides possible explanations for our experiences while coaching college students with traumatic brain injury (TBI). Method The narrative text provides readers with lessons we learned as speech-language pathologists functioning as cognitive coaches to college students with TBI. This is not meant to be an exhaustive list, but rather to consider the recent scientific evidence that will help our understanding of how best to coach these college students. Conclusion Four lessons are described. Lesson 1 focuses on the value of self-reported responses to surveys, questionnaires, and interviews. Lesson 2 addresses the use of immediate/proximal goals as leverage for students to update their sense of self and how their abilities and disabilities may alter their more distal goals. Lesson 3 reminds us that teamwork is necessary to address the complex issues facing these students, which include their developmental stage, the sudden onset of trauma to the brain, and having to navigate going to college with a TBI. Lesson 4 focuses on the need for college students with TBI to learn how to self-advocate with instructors, family, and peers.

Evaluating the Cognitive Interviewing Reporting Framework (CIRF) by Rewriting a Dutch Pretesting Report of a European Health Survey Questionnaire *The views expressed in this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands.

Methodology ◽  
2013 ◽  
Vol 9 (3) ◽  
pp. 104-112 ◽  
Author(s):  
Rachel Vis-Visschers ◽  
Vivian Meertens
Keyword(s):  
Health Survey ◽  
Cognitive Interviewing ◽  
Survey Questionnaire ◽  
Reporting Framework ◽  
Research Designs ◽  
European Health ◽  
Original Report ◽  
Minimal Standard ◽  
Exhaustive List

We used the Cognitive Interviewing Reporting Framework (CIRF) to restructure the report of a pretest on a European health survey questionnaire. This pretest was conducted by the Questionnaire Laboratory of Statistics Netherlands, and the original report was written according to a standard Statistics Netherlands format for pretesting reports. This article contains the rewritten report with highlights from the case study. The authors reflect on the process of rewriting and the usefulness of the CIRF. We conclude that expanded use of the CIRF as a reporting format for articles on cognitive pretests would enhance international comparability, completeness, and uniformity of research designs, terminology, and reporting. A limitation of the CIRF is that it does not provide an exhaustive list of items that could be included in a report, but it is more a “minimal standard”: that is a report on how a cognitive pretest was conducted should at least contain a description of the CIRF items.

Teaching Bach's Binary Forms

Bach ◽  
2018 ◽  
Vol 49 (2) ◽  
pp. 281
Author(s):  
Brody
Keyword(s):  
Binary Forms

scholarly journals Isolation of viable Babesia bovis merozoites to study parasite invasion

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hassan Hakimi ◽  
Masahito Asada ◽  
Takahiro Ishizaki ◽  
Shinichiro Kawazu
Keyword(s):  
Control Strategies ◽  
Specific Inhibitor ◽  
Babesia Bovis ◽  
Parasite Development ◽  
Mammalian Host ◽  
Bovine Babesiosis ◽  
Binary Forms ◽  
Parasite Invasion ◽  
Dependent Protein ◽  
Basic Biology

AbstractBabesia parasite invades exclusively red blood cell (RBC) in mammalian host and induces alterations to host cell for survival. Despite the importance of Babesia in livestock industry and emerging cases in humans, their basic biology is hampered by lack of suitable biological tools. In this study, we aimed to develop a synchronization method for Babesia bovis which causes the most pathogenic form of bovine babesiosis. Initially, we used compound 2 (C2), a specific inhibitor of cyclic GMP-dependent protein kinase (PKG), and a derivative of C2, ML10. While both inhibitors were able to prevent B. bovis egress from RBC and increased percentage of binary forms, removal of inhibitors from culture did not result in a synchronized egress of parasites. Because using PKG inhibitors alone was not efficient to induce a synchronized culture, we isolated viable and invasive B. bovis merozoites and showed dynamics of merozoite invasion and development in RBCs. Using isolated merozoites we showed that BbVEAP, VESA1-export associated protein, is essential for parasite development in the RBC while has no significant role in invasion. Given the importance of invasion for the establishment of infection, this study paves the way for finding novel antigens to be used in control strategies against bovine babesiosis.

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