EVENT DETAILS AND ABSTRACT

Title: Approximation of schemes over complete local rings
Speaker: Shiji Lyu
Speaker Info: UIC
Brief Description:
Special Note:
Abstract:

Let $k$ be a field and $R$ be the power series ring $k[[T_1,\ldots,T_n]]$. Finite type schemes over $R$ were used in, for example, Hironaka's resolution of singularities and the works of de Fernex-Ein-Mustață on ACC of log canonical thresholds. In this talk, 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.