TOPOLOGICAL NOETHERIANITY OF POLYNOMIAL FUNCTORS
TOPOLOGICAL NOETHERIANITY OF POLYNOMIAL FUNCTORS
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DOI：
10.1090/jams/923
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发表时间：
2019-07-01
影响因子：
3.9
通讯作者：
Draisma, Jan
中科院分区：
文献类型：
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作者：
Draisma, Jan
我们证明了无限域上的任何有限次多项式函子都是拓扑Notherian的。这一定理是由Ananyan-Hochster最近解决了Stillman猜想，以及最近Derksen-Eggermont-Snowden关于立方空间的诺瑟性证明而得到的。通过Erman-Sam-Snowden的工作，我们的定理蕴含了Stillman猜想，以及具有固定次数的生成元的多项式环中更广泛的一类理想不变量的有界性。参考文献
We prove that any finite-degree polynomial functor over an infinite field is topologically Noetherian. This theorem is motivated by the recent resolution, by Ananyan-Hochster, of Stillman’s conjecture; and a recent Noetherianity proof by Derksen-Eggermont-Snowden for the space of cubics. Via work by Erman-Sam-Snowden, our theorem implies Stillman’s conjecture and indeed boundedness of a wider class of invariants of ideals in polynomial rings with a fixed number of generators of prescribed degrees. References