Subfields of number field extensions and quadratic forms
| Thesis title in Czech: | Podtělesa rozšíření číselných těles a kvadratické formy |
|---|---|
| Thesis title in English: | Subfields of number field extensions and quadratic forms |
| Key words: | kvadratická mříž|kompozitum|Galoisova korespondence|diskriminant |
| English key words: | quadratic lattice|compositum|Galois correspondence|discriminant |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 27.01.2022 |
| Date of assignment: | 27.01.2022 |
| Confirmed by Study dept. on: | 11.03.2022 |
| Date and time of defence: | 16.06.2022 08:30 |
| Date of electronic submission: | 12.05.2022 |
| Date of submission of printed version: | 16.05.2022 |
| Date of proceeded defence: | 16.06.2022 |
| Opponents: | Daniel Gil Muňoz, Ph.D. |
| Guidelines |
| A recent approach to the study of universal quadratic forms over number fields extends results from a suitable field of small degree to its field extensions. In doing this, one has to carefully control subfields of the field extension. In the thesis, the student will study general conditions (via Galois theory) on when the general construction goes through, and possibly also apply these results to universal forms. |
| References |
| [1] V. Kala, Universal quadratic forms and elements of small norm in real quadratic fields, Bull. Aust. Math. Soc. 94 (2016), 7 - 14
[2] V. Kala, Number fields without universal quadratic forms of small rank exist in most degrees, preprint [3] V. Kala, J. Svoboda, Universal quadratic forms over multiquadratic fields, Ramanujan J. 48 (2019), 151 - 157 [4] J. Neukirch, Algebraic number theory, Springer-Verlag, Berlin, 1999 |