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SUMMARY:Alice Lin (Harvard)
DTSTART:20220406T140000Z
DTEND:20220406T153000Z
DTSTAMP:20260422T220513Z
UID:STAGE/53
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/53/">H
 eight bounds for nondegenerate varieties</a>\nby Alice Lin (Harvard) as pa
 rt of STAGE\n\nLecture held in Room 2-449 in the MIT Simons Building.\n\nA
 bstract\nWe will prove the Silverman-Tate theorem in Appendix 5 of [DGH]\,
  which upper-bounds the difference between the Neron-Tate height and the W
 eil height of a point $P$ in an abelian scheme $\\pi: \\mathcal{A}\\to S$ 
 in terms of the height of the point $\\pi(P)$ in the base scheme. Then\, w
 e'll apply this result\, together with last week's Proposition 4.1 of [DGH
 ]\, to prove Theorem 1.6 in [DGH]\, which gives a lower bound on the Neron
 -Tate height of $P$ in a nondegenerate subvariety $X$ of $\\mathcal{A}\\to
  S$ in terms of the height of $\\pi(P)$. For this application\, we follow 
 Section 5 of [DGH].\n
LOCATION:https://researchseminars.org/talk/STAGE/53/
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