Ext-groups in the category of strict polynomial functors

Abstract The aim of this paper is to study, by using the mathematical tools developed by Chałupnik, Touzé, and Van der Kallen, the effect of the Frobenius twist on $\operatorname{Ext}$-group in the category of strict polynomial functors. As an application, we obtain explicit formulas of cohomology of the orthogonal groups and symplectic ones.