|Responsables :||F. Delon, M. Dickmann, D. Gondard|
|Email des responsables :||firstname.lastname@example.org|
|Adresse :||Sophie Germain|
|Orateur(s)||Hugo Mariano - Université de Sao Paulo, Brésil,|
|Titre||K-theories and free inductive graded rings in abstract quadratic forms theories|
|Horaire||14:00 à 15:45|
(Joint work with Kaique M.A. Roberto (IME-USP))
We will expand a fundamental tool in algebraic theory of quadratic forms to the more general multivalued setting: the K-theory. We introduce and develop the K-theory of hyperbolic hyperfields that generalize simultaneously Milnor's K-theory and Special Groups K-theory, developed by Dickmann-Miraglia. We develop some properties of this generalized K-theory, that can be seen as a free inductive graded ring, a concept introduced in order to provide a solution to Marshall's Signature Conjecture by Dickmann-Miraglia. Moreover, we will show how the extended version of Arason-Pfister Hauptsatz - presented in the previous talk "Multirings and applications to algebraic theory of quadratic forms, IV" - entails some interesting properties concerning K-theory and Marshall's conjecture.