Abstract quadratic form theory
The main objective of so-called abstract or axiomatic quadratic form theory, is to describe what ring-theoretic properties characterise Witt rings of fields. These properties are then considered as axioms, which are used firstly to recover as much as possible of the classical theory of Witt rings of fields, and secondly to further advance the theory starting from this new point of view.
- Becher, Gładki. Symbol length and stability index, Preprint 2010 (6 p.).
Virtual forms
Quadratic forms are further related to Milnor K-theory modulo 2. It turns out that Milnor K-theory modulo any integer l can be studied with the help of ‘virtual forms’ that are quadratic forms when l = 2.
- Becher. Virtual Forms. Mathematische Zeitschrift 265 (2010): 551-569.