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A motivic Weil height machine for curves

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KAH2 - K-theory, algebraic cycles and motivic homotopy theory

The rational points of a smooth curve over a number field map to the set of augmentations of the associated motivic algebra. An expectation, closely related to Kim’s conjecture, is that the set of augmentations which are locally geometric is equal to the set of rational points. We provide evidence for this expectation by extending aspects of the “Weil height machine” to the set of locally geometric augmentations. This is ongoing joint work with L. Alexander Betts. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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