Algebraic Geometry Seminar

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Date, time & place Tuesday 15:30 - 17:00 Room #122 (Graduate School of Math. Sci. Bldg.)

2018/06/12

15:30-17:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Takahiro Shibata (Kyoto)
Ample canonical heights for endomorphisms on projective varieties (English or Japanese)
[ Abstract ]
Given a smooth projective variety on a number field and an
endomorphism on it, we would like to know how the height of a point
grows by iteration of the action of the endomorphism. When the
endomorphism is polarized, Call and Silverman construct the canonical
height, which is an important tool for the calculation of growth of
heights. In this talk, we will give a generalization of the Call-
Silverman canonical heights for not necessarily polarized endomorphisms,
ample canonical heights, and propose an analogue of the Northcott
finiteness theorem as a conjecture. We will see that the conjecture
holds when the variety is an abelian variety or a surface.