CONTENTSIntroduction.................................................................................................................................. 5Chapter I. Preliminaries oil round and Pfister forms.......................................................... 8Chapter II. Basic properties of the Grothendieck ring......................................................... 11 § 1. Prime ideals in G(F)...................................................................................................... 11 § 2. Elements of special types............................................................................................ 15 § 3. Local properties of G(F)................................................................................................ 20Chapter III. Group structure of G(F) and W(F)....................................................................... 23 §1. General decomposition theorems.............................................................................. 23 § 2. Value sets of binary forms and the group structure of G(F) and W(F)................. 28 § 3. The rank of G(F) and W(F)............................................................................................ 32Chapter IV. Equivalence of fields with respect to quadratic forms.................................... 36 § 1. G-equivalences.............................................................................................................. 36 § 2. W-equivalences.............................................................................................................. 41 § 3. Comparisons.................................................................................................................. 43Chapter V. A Galois correspondence in the quadratic form theory.................................. 46 § 1. The binary case............................................................................................................. 46 § 2. A generalization.............................................................................................................. 54Chapter VI. Field constructions................................................................................................ 57Chapter VII. Open problems..................................................................................................... 60References.................................................................................................................................. 62
@book{bwmeta1.element.zamlynska-59a0024f-2459-49af-9af2-8d53bcf7e04b,
author = {K. Szymiczek},
title = {Quadratic forms over fields},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1977},
zbl = {0371.12017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-59a0024f-2459-49af-9af2-8d53bcf7e04b}
}
K. Szymiczek. Quadratic forms over fields. GDML_Books (1977), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-59a0024f-2459-49af-9af2-8d53bcf7e04b/