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This is an English translation of Nikolai Chebotaryovs paper Die Probleme der modernen Galoisschen Theorie from 1932. An excerpt from this paper was given as a lecture at the International Congress of Mathematicians in Zurich in 1932. With the lecture being given to commememorate the centennial of Evariste Galois death, the paper is a broad survey of various contemporary problems in Galois Theory the author found represented the culminations of work done by Galois and his successors.
We study the relationship between the local and global Galois theory of function fields over a complete discretely valued field. We give necessary and sufficient conditions for local separable extensions to descend to global extensions, and for the l
We present a list of problems in arithmetic topology posed at the June 2019 PIMS/NSF workshop on Arithmetic Topology. Three problem sessions were hosted during the workshop in which participants proposed open questions to the audience and engaged in
For a finite Galois extension of fields L/k with Galois group G, we study a functor from the G-equivariant stable homotopy category to the stable motivic homotopy category over k induced by the classical Galois correspondence. We show that after comp
This paper appeals to the figure of Evariste Galois for investigating the gates between mathematics and their publics. The figure of Galois draws some lines of/within mathematics for/from the outside of mathematics and these lines in turn sketch the
We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. Using a criterion of Vakil and a special position argument due to Schubert, this follows from a particular inequality among Kost