The Pfister Factor Conjecture in Characteristic Two

• Applicant: Professor Dr. Karim Johannes Becher
• Subject Area: Mathematics
• Term: from 2012 to 2016
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 210143344

The aim of this project is to extend the result known as the Pfister Factor Conjecture to cover fields of characteristic 2. This conjecture arose from the theory of compositions of quadratic forms, and it has several equivalent formulations. One of them characterizes Pfister forms by the decomposability of their adjoint algebras with involution into products of quaternion algebras. The proof obtained in 2007 relies on several results on quadratic forms and algebras with involution over function fields of conics, which so far are only available in characteristic different from 2. Liberating results from restrictions on the characteristic is a major thread in the current development of the overarching area of linear algebraic groups. The challenge arises from the fact that most concepts familiar in characteristic different from 2 have more than one natural extension to the general setting. In general the project will investigate quadratic and symmetric bilinear forms, as well as algebras with involution and with quadratic pair. For all those objects the isotropy behavior over function fields of conics shall be studied. By these means it is expected to obtain general decomposability results corresponding in characteristic different from 2 to the Pfister Factor Conjecture.

• DFG Programme: Research Grants
• International Connection: Belgium