| Commutative rings A and B are said to be stably isomorphic if A[X] (polynomial algebra in one variable over A) is isomorphic to B[X].
During my last visit to ISI, I gave a couple of lectures on a simple algebraic proof of the following result by Crachiola and Makar-Limanov using the notion of Locally Nilpotent Derivations (LND).
Theorem: Let k be an algebraically closed field of characteristic zero. Let A, B be finitely generated (affine) domains over k which are stably isomorphic. Then A is isomorphic to B in the following cases: (1) Krull dimension of A is one; (2) A is a polynomial algebra in two variables over k.
I will give two lectures presenting examples due to Crachiola of regular, affine domains A,B of dimension two over k which are not isomorphic but are stably isomorphic. LND again plays a crucial role in the construction of these examples. |