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Suslin Rigidity
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: showed that for an extension :E / F of algebraically closed fields, and an algebraic variety ''X'' / ''F'', there is an isomorphism :K_*(X, \mathbf Z/n) \cong K_*(X \times_F E, \mathbf Z/n), \ i \ge 0 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 . This result has stimulated various other papers. For example show that the base change functor for the mod-''n'' stable A1-homotopy category :\mathrm(F, \mathbf Z/n) \to \mathrm(E, \mathbf Z/n) is fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic K-theory
Algebraic ''K''-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory. Geometric, algebraic, and arithmetic objects are assigned objects called ''K''-groups. These are groups in the sense of abstract algebra. They contain detailed information about the original object but are notoriously difficult to compute; for example, an important outstanding problem is to compute the ''K''-groups of the integers. ''K''-theory was discovered in the late 1950s by Alexander Grothendieck in his study of intersection theory on algebraic varieties. In the modern language, Grothendieck defined only ''K''0, the zeroth ''K''-group, but even this single group has plenty of applications, such as the Grothendieck–Riemann–Roch theorem. Intersection theory is still a motivating force in the development of (higher) algebraic ''K''-theory through its links with motivic cohomology and specifically Chow groups. The subject also includes classical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |