Specialization of ℓ-adic representations of arithmetic fundamental groups and applications to arithmetic of abelian varieties

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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Supra-maximal representations from fundamental groups of punctured spheres to PSL(2,ℝ)

Annales Scientifiques de l École Normale Supérieure ◽

10.24033/asens.2410 ◽

2019 ◽

Vol 52 (5) ◽

pp. 1305-1329

Author(s):

Bertrand DEROIN ◽

Nicolas THOLOZAN

Keyword(s):

Fundamental Groups ◽

Maximal Representations

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QUALITATIVE CHANGES IN RHYTHMIC GYMNASTICS HOOP THROWS FROM THE PERSPECTIVE OF BIOMECHANICAL ANALYSIS

SPORT AND SOCIETY ◽

10.36836/2020/1/10 ◽

2020 ◽

pp. 1-8

Author(s):

Raluca Tanasa

Keyword(s):

Correlation Coefficient ◽

Video Recording ◽

Biomechanical Analysis ◽

Fundamental Groups ◽

Horizontal Distance ◽

Video Recordings ◽

Rhythmic Gymnastics ◽

Female Gymnasts ◽

Execution Technique ◽

Qualitative Changes

Throws and catches in rhythmic gymnastics represent one of the fundamental groups of apparatus actuation. They represent for the hoop actions of great showmanship, but also elements of risk. The purpose of this paper is to improve the throw execution technique through biomechanical analysis in order to increase the performance of female gymnasts in competitions. The subjects of this study were 8 gymnasts aged 9-10 years old, practiced performance Rhythmic Gymnastics. The experiment consisted in video recording and the biomechanical analysis of the element “Hoop throw, step jump and catch”. After processing the video recordings using the Simi Motion software, we have calculated and obtained values concerning: launch height, horizontal distance and throwing angle between the arm and the horizontal. Pursuant to the data obtained, we have designed a series of means to improve the execution technique for the elements comprised within the research and we have implemented them in the training process. Regarding the interpretation of the results, it may be highlighted as follows: height and horizontal distance in this element have values of the correlation coefficient of 0.438 and 0.323, thus a mean significance of 0.005. The values of the arm/horizontal angle have improved for all the gymnasts, the correlation coefficient being 0.931, with a significance of 0.01. As a general conclusion, after the results obtained, it may be stated that the means introduced in the experiment have proven their efficacy, which has led to the optimisation of the execution technique, thus confirming the research hypothesis.

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On Abelian Varieties with Complex Multiplication as Factors of the Jacobians of Shimura Curves

American Journal of Mathematics ◽

10.2307/2374049 ◽

1981 ◽

Vol 103 (4) ◽

pp. 727 ◽

Cited By ~ 15

Author(s):

Haruzo Hida

Keyword(s):

Abelian Varieties ◽

Complex Multiplication ◽

Shimura Curves

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Exploring the landscape of CHL strings on Td

Journal of High Energy Physics ◽

10.1007/jhep08(2021)095 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Anamaría Font ◽

Bernardo Fraiman ◽

Mariana Graña ◽

Carmen A. Núñez ◽

Héctor Parra De Freitas

Keyword(s):

Gauge Group ◽

Moduli Space ◽

Dynkin Diagram ◽

Fundamental Groups ◽

Computer Algorithms ◽

Abelian Gauge ◽

Reduced Rank ◽

Systematic Exploration ◽

String Models ◽

Simply Connected

Abstract Compactifications of the heterotic string on special Td/ℤ2 orbifolds realize a landscape of string models with 16 supercharges and a gauge group on the left-moving sector of reduced rank d + 8. The momenta of untwisted and twisted states span a lattice known as the Mikhailov lattice II(d), which is not self-dual for d > 1. By using computer algorithms which exploit the properties of lattice embeddings, we perform a systematic exploration of the moduli space for d ≤ 2, and give a list of maximally enhanced points where the U(1)d+8 enhances to a rank d + 8 non-Abelian gauge group. For d = 1, these groups are simply-laced and simply-connected, and in fact can be obtained from the Dynkin diagram of E10. For d = 2 there are also symplectic and doubly-connected groups. For the latter we find the precise form of their fundamental groups from embeddings of lattices into the dual of II(2). Our results easily generalize to d > 2.

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