Arithmetic Intersection and a conjecture of Lauter

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Microsoft Research
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Published on ● Video Link: https://www.youtube.com/watch?v=TJeLMyHQyn0


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Motivated by her joint work with H. Cohn on genus two curve crypotosystem, Lauter gave a very inspiring conjecture on the CM value of Igusa invariants. They need to compute these values to construct `good' genus two curves. This conjecture led to study of arithmetic intersection on an arithmetic 3-fold (Hilbert modular surface). Recently, I proved an arithmetic intersection formula, which leads to proof of Lauter's conjecture. The formula also leads to the first non-abelian generalization of the celebrated Chowla-Selberg formula.



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