Research > Task IV: Henselian fields
Task IV: Henselian fields
Description
This is an area of research concerned primarily with the model theory of the padics and fields of formal power series. Elimination of quantifiers play a major role, and has been at the source of various applications (for example, in motivic integration and in the theory of zeta functions of finitely generated groups).
a) Develop geometric model theory
for finite extensions of the padics (with extra sorts).
a) Classify semisimple groups definable
in algebraically closed valued fields (ACVF); classify interpretable simple
groups; prove cell decomposition in ACVF (possible applications to arc spaces;
prove elimination of imaginaries for other important valued structures (e.g.
the padics or ACVF with subanalytic structure). Progress Year 1, Year 2, Year 3, Year 4.

Last updated: September 9 2009 15:49  Please send your corrections to: 