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SUMMARY:Dean Lin (UMass Amherst)
DTSTART:20260915T200000Z
DTEND:20260915T210000Z
DTSTAMP:20261023T170314Z
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 Five College Number Theory
  Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbstract\
 nLet $E$ be an elliptic curve over $\\mathbb{Q}$ with good ordinary reduct
 ion at $p$\, $E[p]$ the $p$-torsion points of $E$ and $\\mathbb{Q}_\\infty
 /\\mathbb{Q}$ 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 dual
  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 th
 is talk\, we will focus on the case $p=2$ case and provide an upper bound 
 for the $\\mu$-invariants. Combining with Greenberg’s result\, we are ab
 le to classify all the elliptic curves with $\\mu$-invariant 0 or 1 under 
 the additional assumptions that $E[4]$ is reducible. This is a joint work 
 with Mulun Yin.\n
LOCATION:https://researchseminars.org/talk/FCNTS/36/
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