BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Dean Lin (UMass Amherst)
DTSTART:20260915T200000Z
DTEND:20260915T210000Z
DTSTAMP:20260915T080050Z
UID:FCNTS/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/36/">O
 n Iwasawa $\\mu$-invariants for Selmer groups over $\\mathbb{Z}_2$-extensi
 ons</a>\nby Dean Lin (UMass Amherst) as part of Pioneer Valley Number Theo
 ry Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstrac
 t\nLet $E$ be an elliptic curve over $\\mathbb{Q}$ with good ordinary redu
 ction at $p$\, $E[p]$ the $p$-torsion points of $E$ and $\\mathbb{Q}_\\inf
 ty/\\mathbb{Q}$ the cyclotomic $\\mathbb{Z}_p$-extension. Further assume $
 E[p]$ is reducible as a $G_\\mathbb{Q}$-representation over $\\mathbb{F}_p
 $. In 1999\, Greenberg offered sufficient conditions for the Pontryagin du
 al of the Selmer group over $\\mathbb{Q}_\\infty$ to have $\\mu$-invariant
  0\, and obtained a lower bound when the $\\mu$-invariant is positive. In 
 this talk\, we will focus on the case $p=2$ case and provide an upper boun
 d for the $\\mu$-invariants. Combining with Greenberg’s result\, we are 
 able to classify all the elliptic curves with $\\mu$-invariant 0 or 1 unde
 r the additional assumptions that $E[4]$ is reducible. This is a joint wor
 k with Mulun Yin.\n
LOCATION:https://researchseminars.org/talk/FCNTS/36/
END:VEVENT
END:VCALENDAR