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Session I.2 - Computational Number Theory

Tuesday, June 13, 17:30 ~ 18:00

Limit periods on curves and arithmetic heights

Emre Sertöz

Leibniz University Hannover, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We recently proved that in a nodal degeneration of smooth curves, the periods of the resulting limit mixed Hodge structure (LMHS) contain arithmetic information. For instance, if the nodal fiber is identified with a smooth curve C glued at two points p and q then the LMHS relates to the Neron--Tate height of p-q in the Jacobian of C. In making this relation precise, we observed that a "tropical correction term" is required that is based on finite reductions of the degenerate fiber. In this talk, I will explain this circle of ideas with a focus on the explicit and computable aspects.

Joint work with Spencer Bloch (University of Chicago) and Robin de Jong (Leiden University).

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