Rigidity (K-theory)

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 of algebraically closed fields, and an algebraic variety X / F, there is an isomorphism 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).

For example Röndigs & Østvær (2008) show that the base change functor for the mod-n stable A1-homotopy category is fully faithful.

A similar statement for non-commutative motives has been established by Tabuada (2018).

Another type of rigidity relates the mod-n K-theory of an henselian ring A to the one of its residue field A/m.

Jardine (1993) used Gabber's and Suslin's rigidity result to reprove Quillen's computation of K-theory of finite fields.