Supreme torsion forms

Abstract

We study formally real, non-pythagorean fields which have an anisotropic torsion form that contains every anisotropic torsion form as a subform. We obtain consequences for certain invariants and the Witt ring of such fields and construct examples. We obtain a theory analogous to the theory of supreme Pfister forms introduced by Karim Becher and see examples in which the Pythagoras number for formally real fields behaves like the level for nonreal fields.

Keywords:

• formally real field
• Pfister form
• Pythagoras number
• quadratic form
• Witt ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 11E81
• 11E10

Acknowledgments

The results contained in this paper are part of the PhD-Thesis of the author. He would like to thank Detlev Hoffmann for supervising this work and giving some very useful hints and corrections in the process. Furthermore, he wants to thank the referee for carefully reading the manuscript and providing many improvements.