Carlos Rivera's Defense: 10am tomorrow (August 15) in PDL C38

[Bianca Viray]

Hi all,

Those of you who are around in the summer quarter may be interested in Carlos Rivera's defense talk tomorrow (August 15th) at 10:00 am in PDL C38. His thesis title and abstract are below.

Reciprocity and local to global principles on $p$-adic function fields

In 2021, Olivier Wittenberg introduced a new obstruction to the local to global principle for varieties over $p$-adic function fields, the reciprocity obstruction, analogue to the Brauer-Manin obstruction for number fields, but unlike previous versions of it, including all divisorial valuation of the $p$-adic function field. We show a refinement theorem for the obstruction over blow ups of integral models of the $p$-adic function field, compare the obstruction with previous ones, construct some examples, and show the obstruction is the only one for connected $0$-dimensional varieties. We also define a reciprocity obstruction to the field patching method of Harbarter, Hartmann and Krashen, and use the refinement theorem to show it agrees with Wittenberg's version when both apply. This reduces the computation of the reciprocity pairings over all closed points of all integral models to a finite one. Finally, we analyse the existence of patch points in the field patching method from an analytic point of view, providing a conjectural reason for their existence.

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Bianca Viray (she/her)

Craig McKibben and Sarah Merner Professor of Mathematics

University of Washington

Seattle, WA 98195

https://sites.math.washington.edu/~bviray/