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SUMMARY:Group actions on curves and applications [MPIM]
DTSTART:20260825T120000Z
DTEND:20260825T130000Z
DTSTAMP:20260822T142500Z
UID:indico-event-1543@math-events.uni-bonn.de
DESCRIPTION:Speakers: Alexandros Konstantinou (MPIM)\n\nPLeaSANT\nIn this 
 talk we will focus on one arithmetic setting: the action of a finite group
  G on a curve X. The idea is to pass to its Jacobian variety and let the r
 epresentation theory of G do the work. This splits the Jacobian\, up to is
 ogeny\, into smaller factors. We will explain this method and give some ex
 amples.\nAs an application\, I will turn to Tate--Shafarevich groups. Thes
 e play an important role in the study of rational points on abelian variet
 ies\, but they are notoriously difficult to compute\, or even to prove fin
 ite. For an elliptic curve\, the Tate--Shafarevich group has square order 
 when finite. This is not always true for abelian varieties of higher dimen
 sion\, a fact that was long overlooked and often misstated in the literatu
 re. We will show that every square-free positive integer appears as the sq
 uare-free part of the order of the Tate--Shafarevich group of an abelian v
 ariety over the rationals.\n\nhttps://math-events.uni-bonn.de/event/1543/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1543/
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