Topological galois theory pdf

Abstract topological methods in galois theory yuri burda doctor of philosophy graduate department of mathematics university of toronto 2012 this thesis is devoted to application of topological ideas to galois theory. In particular, it offers a complete exposition of the relatively new area of topological galois theory, initiated by the author. Motivated by the extension of classical galois theory by h. Galois theory for schemes of websites universiteit leiden. Semi topological galois theory and the inverse galois problem article pdf available in algebra colloquium january 20 with 33 reads how we measure reads. New topological contexts for galois theory and algebraic. Topological galois theory problems of solvability and nonsolvability of algebraic, transcendental and di erential equations inexplicit form, including liouville theory, classical and di erential galois theory, and picardvessiot theory, will be addressed from the geometry and analysis point of view.

Our framework subsumes in particular grothendiecks galois theory and allows to build. K yn wab k where wab k is the abelianization of the weil group w k see. Moore and seiberg equations, topological field theories and galois theory. Algebra and representation theory in modular tensor categories can be. Local class eld theory gives an isomorphism of topological groups art k. Classes of topological groups suggested by galois theory.

Pdf moore and seiberg equations, topological field. Topological galois theory olivia caramello january 2, 20 abstract we introduce an abstract topostheoretic framework for building galois type theories in a variety of di. As khovanskii writes in the introduction to his new book topological galois theory, according to this theory, the way the riemann surface of an analytic function covers the plane of complex numbers can obstruct the representability of this function by explicit formulas. The strongest known results on the unexpressibility of functions by. The local langlands conjecture is inspired by the result for gl 1pkq, namely local class eld theory. Here we focus solely on the case g gl nand kis a padic eld such as q p. These notes give a concise exposition of the theory of. Some aspects of topological galois theory sciencedirect. New topological contexts for galois theory and algebraic geometry andrew baker university of glasgow, birgit richter universit.