Classification of quadratic forms over Q

Bogliolo, Elena (2021) Classification of quadratic forms over Q. [Laurea], Università di Bologna, Corso di Studio in Matematica [L-DM270]
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The objective of this thesis is the complete classification of quadratic forms over the field of rational numbers. This is achieved by proving the Theorem of Hasse-Minkowski that, given a homogeneous second degree polynomial f, builds a correspondence between the roots of f over the p-adic fields and the roots of f over the rational numbers. The p-adic fields are presented as completions of the rational field with respect to the p-adic absolute values. Using the discriminant and Hasse-Minkowski invariant, a complete classification of the quadratic forms over the p-adic fields is achieved. From these results it is possible to find whether or not two quadratic forms are equivalent over the rational field by computing countable invariants.

Tipologia del documento
Tesi di laurea (Laurea)
Autore della tesi
Bogliolo, Elena
Relatore della tesi
Corso di studio
Ordinamento Cds
Parole chiave
classification invariants quadratic forms forme quadratiche Hilbert Hasse-Minkowski p-adic
Data di discussione della Tesi
23 Luglio 2021

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