Institute of Mathematics for Industry

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Northcott numbers for the weighted Weil heights


Hold Date 2022-07-01 15:00~2022-07-01 16:00

Place C-513 and Zoom meeting

Object person  

Speaker Kaoru Sano (Doshisha University)

In the field of Diophantine Geometry, the absolute Weil height function is an important tool to prove various finiteness property. For a given set of algebraic numbers, the infimum of upper bounds on heights for which the finiteness holds is called Northcott number. Vidaux-Videla asked that whether there exists an algebraic field such that the Northcott number is equal to the given constant. Pazuki-Technau-Widmer defined weighted Weil heights interpolating absolute and relative heights. In collaboration with Okazaki, we completely answered to the Vidaux-Videla’s question and obtained a further generalization for weighted heights. In this talk, I will present the results and background.