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摘要翻译：
将Kohn有限理想型和D'Angelo有限型与$\bar\部分$-Neumann问题的次椭圆性的等价性推广到$C^n$中的伪凸域，其定义函数为一个在微分下闭的Denjoy-Carleman拟解析类。这个证明涉及到Denjoy-Carleman拟解析函数的芽环上的代数几何，该芽环是介于实解析函数的芽环和光滑函数的芽环之间的，不是已知的Noetherian。本文还证明了这类Denjoy-Carleman函数的芽环满足$\sqrt{acc}$性质，这是非诺以太环所能具有的最强性质之一。
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英文标题：
《The Kohn Algorithm on Denjoy-Carleman Classes》
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作者：
Andreea C. Nicoara
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最新提交年份：
2014
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分类信息：
一级分类：Mathematics 数学
二级分类：Complex Variables 复变数
分类描述：Holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves
全纯函数，自守群作用与形式，伪凸性，复几何，解析空间，解析束
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
The equivalence of the Kohn finite ideal type and the D'Angelo finite type with the subellipticity of the $\bar\partial$-Neumann problem is extended to pseudoconvex domains in $C^n$ whose defining function is in a Denjoy-Carleman quasianalytic class closed under differentiation. The proof involves algebraic geometry over a ring of germs of Denjoy-Carleman quasianalytic functions that is not known to be Noetherian and that is intermediate between the ring of germs of real-analytic functions and the ring of germs of smooth functions. It is also shown that this type of ring of germs of Denjoy-Carleman functions satisfies the $\sqrt{acc}$ property, one of the strongest properties a non-Noetherian ring could possess.
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PDF链接：
https://arxiv.org/pdf/0806.1917
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