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DTSTART:20211107T020000
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UID:calendar.25212.field_event_date_2.0@math.wustl.edu
CREATED:20211104T154323Z
DESCRIPTION:Abstract: Let X be a smooth projective variety over an algebrai
c number field F. We say that X satisfies Weak Approximation if the set X
(F) of all F-rational points on X is dense inside the product of all X(F_v
), where v runs through the set of all places of F. That is, in some app
ropriate sense, every family of local points can be 'approximated' by a g
lobal point. By the foundational work of Y. Manin, the Brauer group of X
often obstructs Weak Approximation and for certain classes of varieties th
is obstruction is known or conjectured to fully explain the failure. In ot
her words, every family of local points that is orthogonal to the Brauer
group can be approximated by a global point. In this talk I will discuss a
nalogs of these questions for the Chow group CH_0(X) of zero-cycles on X.
In the 1980's Colliot-Thelene, Sansuc, Kato and Saito conjectured that
the Brauer group should give the only obstruction to Weak Approximation f
or zero-cycles when X is a general smooth projective variety. This conject
ure has only been established for certain classes of rationally connected
varieties, and there is some recent partial evidence for products of K3 s
urfaces. The purpose of this talk will be to give some evidence for a prod
uct of elliptic curves. Part of this talk will be based on recent joint w
ork with Toshiro Hiranouchi, and another part is work in progress with an
Appendix by Angelos Koutsianas. \n\nHost: Humberto Diaz
DTSTART;TZID=America/Chicago:20211110T160000
DTEND;TZID=America/Chicago:20211110T170000
LAST-MODIFIED:20211104T163042Z
SUMMARY:Algebraic Geometry Seminar: 'Local-to-global principles for zero-cy
cles'
URL;TYPE=URI:https://math.wustl.edu/events/algebraic-geometry-seminar-local
-global-principles-zero-cycles
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