Automorphism groups of transcendental field extensions

Abstract: It is well-known that the Galois group of an (infinite) algebraic field extension is a profinite group. When the extension is transcendental, the automorphism group is no longer compact, but has a totally disconnected locally compact structure (TDLC for short). The study of TDLC groups was initiated by van Dantzig in 1936 and then restarted by Willis in 1994. In this talk some of Willis' concepts, such as tidy subgroups, the scale function, flat subgroups and directions are introduced and applied to examples of automorphism groups of transcendental field extensions. It remains unknown whether there exist conditions that a TDLC group must satisfy to be a Galois group. A suggestion of such a condition is made.

group theory

Audience: researchers in the discipline

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