# Linkage of quadratic Pfister forms

`2017-01-18 10:30:00``2017-01-18 11:30:00``Linkage of quadratic Pfister forms``Quadratic Pfister forms are a special class of quadratic forms that arise naturally as norm forms of composition algebras. The Witt group I_q F of quadratic forms (modulo hyperbolic forms) over a field F is a module over the Witt ring of bilinear forms. This gives a most important filtration { I_q^n F }. The n-fold Pfister forms, which are tensor products of n Pfister forms, generate I_q^n F. We call a set of quadratic n-fold Pfister forms linked if they all share a common (n-1)-fold Pfister factor. Since we wish to develop a characteristic-free theory, we need to consider the characteristic 2 case, where one has to distinguish between right linkage and left linkage. To a certain type of set of s n-fold Pfister forms, we associate an invariant in I_q^{n+1} F which lives in I_q^{n+s-1} F when the set is linked. We study the properties of this invariant and compute necessary conditions for a set to be linked. We also consider the related notion of linkage for quaternion algebras via linkage of the associated norm forms.``Third floor seminar room``אוניברסיטת בר-אילן - Department of Mathematics``mathoffice@math.biu.ac.il``Asia/Jerusalem``public`Quadratic Pfister forms are a special class of quadratic forms that arise naturally as norm forms of composition algebras. The Witt group I_q F of quadratic forms (modulo hyperbolic forms) over a field F is a module over the Witt ring of bilinear forms. This gives a most important filtration { I_q^n F }. The n-fold Pfister forms, which are tensor products of n Pfister forms, generate I_q^n F.

We call a set of quadratic n-fold Pfister forms linked if they all share a common (n-1)-fold Pfister factor. Since we wish to develop a characteristic-free theory, we need to consider the characteristic 2 case, where one has to distinguish between right linkage and left linkage.

To a certain type of set of s n-fold Pfister forms, we associate an invariant in I_q^{n+1} F which lives in I_q^{n+s-1} F when the set is linked. We study the properties of this invariant and compute necessary conditions for a set to be linked.

We also consider the related notion of linkage for quaternion algebras via linkage of the associated norm forms.

Last Updated Date : 11/01/2017