论文标题
关于霍维的猜想 - 史蒂克兰和柴
On conjectures of Hovey--Strickland and Chai
论文作者
论文摘要
我们证明了两个猜想的霍维和斯特里克兰的高度，该猜想提供了$ k（n）$ - 霍普金斯的本地类似物 - 史密斯厚的子类别定理。我们的方法首先将一般的猜想降低为柴ai造成的算术几何形状的问题。然后，我们使用毛 - 霍普金斯时期地图来验证Chai在高度二和所有素数上的希望。在此过程中，我们证明了Morava $ e $ $ $ - 理论的分级合作的划分的交换戒指是连贯的，并且每个有限生成的Morava模块都可以通过$ k（n）$ - 本地频谱实现，长达$ 2P-2> $ 2p-2> n^2+n $。最后，我们将结果的后果推断为Balmer光谱的后裔。
We prove the height two case of a conjecture of Hovey and Strickland that provides a $K(n)$-local analogue of the Hopkins--Smith thick subcategory theorem. Our approach first reduces the general conjecture to a problem in arithmetic geometry posed by Chai. We then use the Gross--Hopkins period map to verify Chai's Hope at height two and all primes. Along the way, we show that the graded commutative ring of completed cooperations for Morava $E$-theory is coherent, and that every finitely generated Morava module can be realized by a $K(n)$-local spectrum as long as $2p-2>n^2+n$. Finally, we deduce consequences of our results for descent of Balmer spectra.
