Approximation of complete local rings - Shiji Lyu скачать в хорошем качестве

Approximation of complete local rings - Shiji Lyu

Title: Approximation of complete local rings Abstract: For simplicity, let R be a power series ring over a field k. We discuss a systematic way of approximating finite type schemes over R using schemes essentially of finite type over k, preserving various types of singularities and homological properties. This allows us to extend known results and constructions for varieties to finite type schemes over R, including formulas for multiplier ideals, deformation of singularities, and big Cohen-Macaulay algebras. The method works in other situations as well, giving other consequences, for example in étale cohomology. This is joint work in preparation with Shizhang Li and Bogdan Zavyalov.