Thesis (Selection of subject)Thesis (Selection of subject)(version: 285)
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Composition of quadratic forms over number fields
Thesis title in Czech: Skládání kvadratických forem nad číselnými tělesy
Thesis title in English: Composition of quadratic forms over number fields
Key words: binární kvadratické forma, třídová grupa, číselné těleso, Bhargavova krychle
English key words: binary quadratic form, ideal class group, number field, Bhargava cube
Academic year of topic announcement: 2017/2018
Type of assignment: diploma thesis
Thesis language: angličtina
Department: Department of Algebra (32-KA)
Supervisor: Mgr. Vítězslav Kala, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 04.10.2017
Date of assignment: 04.10.2017
Confirmed by Study dept. on: 27.11.2017
Date and time of defence: 14.06.2018 09:00
Date of electronic submission:01.05.2018
Date of submission of printed version:11.05.2018
Date of proceeded defence: 14.06.2018
Reviewers: Pavel Francírek
M. Bhargava recently found a new view on Gauss composition of binary quadratic forms through certain "cubes of integers". M. W. Mastropierto proved the correspondence between the ideal class group and binary quadratic forms (and hence the Gauss composition) over real quadratic fields of class number one. The goal of the thesis is to study and connect these two results: to generalize Gauss composition to more general number fields, and to possibly try to use it for a generalization of the composition of Bhargava cubes.
[1] Bhargava, M.: Higher composition laws I: A new view on Gauss composition, and quadratic generalizations, Ann. of Math., 159 (2004), pp. 217–250
[2] Mastropierto, M. W.: Quadratic Forms and Relative Quadratic Extensions, dissertation, 2000,
[3] O'Dorney, E.: Rings of small rank over a Dedekind domain and their ideals, 2015, arXiv:1508.02777
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