Rigidity (K-theory)
In mathematics, rigidity of K-theory encompasses results relating algebraic K-theory of different rings. == Suslin rigidity == Suslin rigidity, named after Andrei Suslin, refers to the invariance of mod-n algebraic K-theory under the base change between two algebraically closed fields: Suslin (1983) showed that for an extension E / F {\displaystyle E/F} of algebraically closed fields, and an algebraic variety X / F, there is an isomorphism K ∗ ( X , Z / n ) ≅ K ∗ ( X × F E , Z / n ) , {\displaystyle K_{*}(X,\mathbf {Z} /n)\cong K_{*}(X\times _{F}E,\mathbf {Z} /n),} between the mod-n K-theory of coherent sheaves on X, respectively its base change to E. A textbook account of this fact in the case X = F, including the resulting computation of K-theory of algebraically closed fields in characteristic p, is in Weibel (2013).