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SUMMARY:Yu Fu (California Institute of Technology)
DTSTART:20231031T210000Z
DTEND:20231031T220000Z
DTSTAMP:20260423T024839Z
UID:UAANTS/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/78/">
 How do generic properties spread?</a>\nby Yu Fu (California Institute of T
 echnology) as part of University of Arizona Algebra and Number Theory Semi
 nar\n\nLecture held in ENR2 S395.\n\nAbstract\nGiven a family of algebraic
  varieties\, a natural question to ask is what type of properties of the g
 eneric fiber\, and how those properties extend to other fibers. Let's expl
 ore this topic from an arithmetic point of view by looking at the scenari
 o: Suppose we have a 1-dimensional family of pairs of elliptic curves ove
 r a number field $K$\,  with the generic fiber of this family being a pai
 r of non-isogenous elliptic curves. Furthermore\, suppose the (projective)
  height of the parametrizer is less than or equal to $B$. One may ask how 
 does the property of "being isogenous" extends to the special fibers. Can 
 we give a quantitative estimation for the number of specializations of hei
 ght at most $B$\, such that the two elliptic curves at the specializations
  are isogenous?\n
LOCATION:https://researchseminars.org/talk/UAANTS/78/
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