论文标题
闭合理论证明了常规环中符号力的统一界限
Closure-theoretic proofs of uniform bounds on symbolic powers in regular rings
论文作者
论文摘要
我们为统一的界限提供了简短的封闭理论证明，以实现常规环中理想的符号能力的增长。作者最近使用了多种版本的PerfectOid/Big Cohen-Macaulay测试理想证明了这些界限，并由MA和Schwede较早获得。在混合特征中，我们相反，我们使用Heitmann的完整扩展加上（EPF）闭合，江外的EPF（WEPF）闭合（WEPF）闭合，以及R.G.的结果，可诱导大型Cohen-Macaulay代数的封闭操作。我们的策略还适用于满足R.G.代数公理和Briançon-Skoda型定理的任何闭合，因此，在所有特征的常规环中，理想的符号能力的增长均基于统一的界限。在同等的特征上，这些符号力量的结果是由于Ein Lazarsfeld-Smith，Hochster-Huneke，Takagi-Yoshida和Johnson所致。
We give short, closure-theoretic proofs for uniform bounds on the growth of symbolic powers of ideals in regular rings. The author recently proved these bounds in mixed characteristic using various versions of perfectoid/big Cohen-Macaulay test ideals, with special cases obtained earlier by Ma and Schwede. In mixed characteristic, we instead use Heitmann's full extended plus (epf) closure, Jiang's weak epf (wepf) closure, and R.G.'s results on closure operations that induce big Cohen-Macaulay algebras. Our strategy also applies to any Dietz closure satisfying R.G.'s algebra axiom and a Briançon-Skoda-type theorem, and hence yields new proofs of these results on uniform bounds on the growth of symbolic powers of ideals in regular rings of all characteristics. In equal characteristic, these results on symbolic powers are due to Ein-Lazarsfeld-Smith, Hochster-Huneke, Takagi-Yoshida, and Johnson.
