BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Bryden Cais (University of Arizona)
DTSTART:20240123T210000Z
DTEND:20240123T220000Z
DTSTAMP:20260423T041524Z
UID:UAANTS/84
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/84/">
 Iwasawa theory for class group schemes in characteristic p</a>\nby Bryden 
 Cais (University of Arizona) as part of University of Arizona Algebra and 
 Number Theory Seminar\n\nLecture held in ENR2 S395.\n\nAbstract\nIn a land
 mark 1959 paper\, Iwasawa studied the growth of class groups in Z_p-towers
  of number fields\, establishing a remarkable formula for the exact power 
 of p dividing the order of the class group of the n-th layer of the tower.
  Iwasawa's work was inspired by a profound analogy between number fields a
 nd function fields over finite fields. In this setting\, the direct analog
 ue of Iwasawa theory is the study of class groups in Z_p-towers of global 
 function fields over finite fields k of characteristic p\, and an analogou
 s formula for the order of p dividing the class group was established by M
 azur and Wiles in 1983. An extraordinary feature of this function field se
 tting is that the class group can be realized as the k-rational points of 
 an algebraic variety---the Jacobian.  We will briefly survey some of this 
 history\, and introduce a novel analogue of Iwasawa theory for function fi
 elds by studying not just the k-points of these Jacobians\, but their full
  p-torsion group schemes\, which are much richer\, geometric objects havin
 g no analogue in the number field setting.\n
LOCATION:https://researchseminars.org/talk/UAANTS/84/
END:VEVENT
END:VCALENDAR