Tel Aviv University
The next colloquium talk will be held on Monday, 12/12/2011, 12:15,
Schreiber 006, Tel Aviv University. The speaker is
Elad Paran (Open University of Israel)
and the title of his talk is
A unified approach to the patching of Galois groups
The abstract is given below. Tea and coffee at 12:00, same room.
Hope to see you there. For information about future colloqiua, see
You are all welcome to suggest colloquium speakers, especially for the end
of January and for the second semester.
Abstract: A central conjecture in modern Galois theory asserts that every
finite group occurs as a Galois group over the field of rational functions
K(x), for every field K. While in general the conjecture is wide open, for
large classes of important fields it is known to hold, most notably whenever
K is complete with respect to an absolute value. The "archimedean" case of
this theorem (where K is the field of real or complex numbers) is a
consequence of Riemann's Existence Theorem and methods of complex topology.
The non-archimedean case (where K is a local field) was proven in 1984 by
Harbater, using methods of formal geometry, most notably Grothendieck's
Harbater's constructions draw inspriation from the mentioned complex
topological methods, but the analogy between these situations is quite
limited and not fully understood. In this work we present a new approach
which allows for a uniform proof of the theorem (and more). The central idea
is to use a new type of objects in order to patch Galois groups -- Wiener
Algebras (an object arising from Harmonic analysis). The proof via this
approach is essentially elementary, relying on no deep theorems.
No background is assumed.
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel <email@example.com>
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