UCLA

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.