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SUMMARY:Jeremy Booher (University of Canterbury)
DTSTART:20210119T210000Z
DTEND:20210119T213000Z
DTSTAMP:20260423T021229Z
UID:POINT/26
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/26/">I
 nvariants in Towers of Curves over Finite Fields</a>\nby Jeremy Booher (Un
 iversity of Canterbury) as part of POINT: New Developments in Number Theor
 y\n\n\nAbstract\nA $Z_p$ tower of curves in characteristic $p$ is a sequen
 ce $C_0\, C_1\, C_2\, ...$ of smooth projective curves over a perfect fiel
 d of characteristic $p$ such that $C_n$ is a branched cover of $C_{n-1}$ a
 nd $C_n$ is a branched Galois $Z/(p^n)$-cover of $C_0$.  For nice examples
  of $Z_p$ towers\, the growth of the genus is stable: for sufficiently lar
 ge $n$\, the genus of $C_n$ is a quadratic polynomial in $p^n$.  In charac
 teristic $p$\, there are additional curve invariants like the a-number whi
 ch are poorly understood.  They describe the group-scheme structure of the
  $p$-torsion of the Jacobian.  I will discuss work in progress with Bryden
  Cais studying these invariants and suggesting that their growth is also s
 table in genus stable $Z_p$ towers.  This is a new kind of Iwasawa theory 
 for function fields.\n\nTo join the talks on January 19th\, please registe
 r here:  \n\nhttps://ucsd.zoom.us/meeting/register/tJIuf-6uqjoiH9eVbtLN9y1
 G9l0qEBmbDRmV\n
LOCATION:https://researchseminars.org/talk/POINT/26/
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