A non-standard proof of the Briançon-Skoda theorem
A non-standard proof of the Briançon-Skoda theorem
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 …