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TZID:America/Chicago
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DTSTART:20231105T020000
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DTSTART:20230312T020000
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UID:calendar.25875.field_event_date_2.0@math.wustl.edu
CREATED:20230922T192419Z
DESCRIPTION:Abstract:\n\nGiven an abelian variety $A$ defined over a number
field, a conjecture attributed to Serre states that the set of primes at
which $A$ admits ordinary reduction is of positive density. This conjectu
re had been proved for elliptic curves (Serre, 1977), abelian surfaces (
Katz 1982, Sawin 2016) and certain higher dimensional abelian varieties (
Pink 1983, Fite 2021, etc). \n\nIn this talk, we will discuss ideas beh
ind these results and recent progress for abelian varieties with non-trivi
al endomorphisms, including the case where $A$ has almost complex multipl
ication by an abelian CM field, based on joint work with Cantoral-Farfan\
, Mantovan, Pries, and Tang.\n\nApart from ordinary reduction, we will
also discuss the set of primes at which an abelian variety admits basic re
duction, generalizing a result of Elkies on the infinitude of supersingul
ar primes for elliptic curves. This is joint work with Mantovan, Pries,
and Tang.
DTSTART;TZID=America/Chicago:20230927T160000
DTEND;TZID=America/Chicago:20230927T170000
LAST-MODIFIED:20230927T163136Z
SUMMARY:AAG Seminar: Basic reductions of abelian varieties
URL;TYPE=URI:https://math.wustl.edu/events/aag-seminar-basic-reductions-abe
lian-varieties
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