Second order differential equations and projective connections

Abstract: Reference: Deligne, Section 5.

In the previous section, Deligne sets up an equivalence of categories between order-n differential equations on line bundles on curves and rank-n vector bundles with connection plus the extra data of a certain cyclic morphism.

In section 5, Deligne reinterprets the special case n = 2 in terms of a connection on a certain bundle and another uniformization datum called a projective connection. I will prove this alternative equivalence of categories, focusing on the different ways of viewing and computing with projective connections.

algebraic geometrynumber theory

Audience: advanced learners

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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.

Fall 2025 topic: Weil conjectures.

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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