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Daily Overview |
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AG1: Algebraic Geometry Location: A701 Session Chair: Mateusz Michalek Session Chair: Botong Wang | |
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Noetherianity up to Sym and GL 1: University of Bern, Switzerland; 2: University of Michigan, USA; 3: Eindhoven University of Technology, The Netherlands Work by Daniel Cohen from the 1980s implies that, if X is an affine scheme of finite type over a Noetherian ring, then the infinite Cartesian product XN (N={the natural numbers}) is Noetherian up to the infinite symmetric group Sym: every descending chain of Sym-stable closed subschemes is eventually constant. A similar result holds for GL-varieties, infinite-dimensional affine varieties with a suitable action of the infinite general linear group, albeit only for reduced subschemes. Both of these results have led to much follow-up work and applications. I will discuss some of this work and then move on to the following "least common multiple" of both results above: if X is a GL-variety, then XN is Noetherian up to the product Sym x GL. This theorem is joint work with Chiu, Danelon, Eggermont, and Farooq—and it is waiting for good applications! | |
