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SUMMARY:Katharina Müller (University Göttingen)
DTSTART:20201117T093000Z
DTEND:20201117T100000Z
DTSTAMP:20260423T021248Z
UID:POINT/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINT/20/">T
 he split prime $\\mathbb{Z}_p$-extension of imaginary quadratic fields</a>
 \nby Katharina Müller (University Göttingen) as part of POINT: New Devel
 opments in Number Theory\n\n\nAbstract\nLet $K$ be an imaginary quadratic 
 field and $p$ a rational prime that splits into $p_1$ and $p_2$. Then ther
 e is a unique $\\mathbb{Z}_p$ extension that is only ramified at one of th
 e primes above $p$. We will shift this extension by an abelian extension o
 ver $L/ K$ to $L_{\\infty}$. Let $M$ be the maximal $p$-abelian $p_1$-rami
 fied extension of $L_{\\infty}$. Generalizing work of Schneps we will show
  that $Gal(M/L_{\\infty})$ is a finitely generated $\\mathbb{Z}_p$-module.
  If time allows we will also discuss the main conjecture for these extensi
 ons. Part of this talk is joint work with Vlad Crisan.\n
LOCATION:https://researchseminars.org/talk/POINT/20/
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