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SUMMARY:Jeremy Booher (University of Canterbury)
DTSTART:20220215T023000Z
DTEND:20220215T040000Z
DTSTAMP:20260423T041525Z
UID:viasmag/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/viasmag/6/">
 Iwasawa Theory for $p$-torsion Class Group Schemes in Characteristic $p$</
 a>\nby Jeremy Booher (University of Canterbury) as part of VIASM Arithmeti
 c Geometry Online Seminar\n\nLecture held in C101\, VIASM.\n\nAbstract\nA 
 $\\mathbb{Z}_p$ tower of curves in characteristic $p$ is a sequence $C_0\,
  C_1\, C_2\, \\ldots$ of smooth projective curves over a perfect field of 
 characteristic $p$ such that $C_n$ is a branched cover of $C_{n-1}$ and $C
 _n$ is a branched Galois $\\mathbb{Z}/(p^n)$-cover of $C_0$.  The genus is
  a well-understood invariant of algebraic curves\, and the genus of $C_n$ 
 can be seen to depend on $n$ in a simple fashion.  In characteristic $p$\,
  there are additional curve invariants like the $a$-number which are poorl
 y understood. They describe the group-scheme structure of the $p$-torsion 
 of the Jacobian. I will discuss work with Bryden Cais studying these invar
 iants and suggesting that their growth is also "regular" in $\\mathbb{Z}_p
 $ towers. This is a new kind of Iwasawa theory for function fields.\n
LOCATION:https://researchseminars.org/talk/viasmag/6/
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