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- W1551115927 abstract "Using a tight closure argument in characteristic $p$ and then lifting the argument to characteristic zero with the aid of ultraproducts, I present an elementary proof of the Briançon-Skoda Theorem: for an $m$-generated ideal $mathfrak {a}$ of ${mathbb C}[[{X_1,dots ,X_n}]]$, the $m$-th power of its integral closure is contained in $mathfrak {a}$. It is well-known that as a corollary, one gets a solution to the following classical problem. Let $f$ be a convergent power series in $n$ variables over $mathbb C$ which vanishes at the origin. Then $f^n$ lies in the ideal generated by the partial derivatives of $f$." @default.
- W1551115927 created "2016-06-24" @default.
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- W1551115927 date "2002-05-29" @default.
- W1551115927 modified "2023-09-23" @default.
- W1551115927 title "A non-standard proof of the Briançon-Skoda theorem" @default.
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- W1551115927 doi "https://doi.org/10.1090/s0002-9939-02-06556-5" @default.
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