Peter McDonald

The Briançon-Skoda theorem is a comparison relating the integral closure of powers of a finitely generated ideal with its ordinary powers. Originally proved using analytic methods for coordinate rings of smooth varieties over the complex numbers in...

In 1974, Briançon and Skoda answered a question of Mather, showing that for $I=(f_1,\dots,f_n)$ an ideal of the coordinate ring at a smooth point on a complex algebraic variety, there is a containment $\overline{I^{n+k-1}}\subseteq I^k$ for all $k...

The Direct Summand Theorem states that if $R$ is a commutative Noetherian ring, then any finite extension $R\to S$ splits as a map of $R$-modules. This suggests the notion of a splinter as a class of singularities, where we say a scheme $X$ is a...