Degree Three Cohomological Invariants and Motivic Cohomology of Reductive Groups
- Author(s): Laackman, Donald Joseph
- Advisor(s): Merkurjev, Alexander S
- et al.
This dissertation is concerned with calculating the group of degree three cohomological
invariants of a reductive group over a ﬁeld of arbitrary characteristic. We prove a formula
for the group of degree three cohomological invariants of a split reductive group G with coeﬃcients in Q/Z(2) over a ﬁeld F of arbitrary characteristic. As an application, we then use this to deﬁne the group of reductive invariants of split semisimple groups, and compute
these groups in all (almost) simple cases. We additionally prove the existence of a discrete
relative motivic complex for any reductive group, which could be used to compute the degree
two and three invariants of arbitrary reductive groups.