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Algebra and Geometry Seminar

Monday, January 13, 2020
4:00pm to 5:00pm
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Linde Hall 255
The section conjecture at the boundary of moduli space
Daniel Litt, Department of Mathematics, University of Georgia,

Grothendieck's section conjecture predicts that over arithmetically interesting fields (e.g. number fields), rational points on a smooth projective curve X of genus at two can be detected via the arithmetic of the etale fundamental group of X. We construct infinitely many curves of each genus satisfying the section conjecture in interesting ways, building on work of Stix, Harari, and Szamuely. The main input to our result is an analysis of the degeneration of certain torsion cohomology classes on the moduli space of curves at various boundary components. This is (preliminary) joint work with Padmavathi Srinivasan, Wanlin Li, and Nick Salter.

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