Alterations

Abstract: In 1964, Hironaka proved that over a field of characteristic zero, every algebraic variety admits a resolution of singularities. However, the problem of resolution of singularities is still open in positive characteristic. As a weaker result, de Jong proved that every algebraic variety admits regular alterations. We will discuss background, main statements and some applications for de Jong's result. If time allows, we will discuss a very rough sketch of the proof.

Reference: Notes from Conrad's lectures on alternations, Section 1. The goal is to understand the statement of the main theorem on alterations.

algebraic geometrynumber theory

Audience: advanced learners

( slides )

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STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

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