The split prime $\mathbb{Z}_p$-extension of imaginary quadratic fields

Katharina Müller (University Göttingen)

17-Nov-2020, 09:30-10:00 (3 years ago)

Abstract: Let $K$ be an imaginary quadratic field and $p$ a rational prime that splits into $p_1$ and $p_2$. Then there is a unique $\mathbb{Z}_p$ extension that is only ramified at one of the primes above $p$. We will shift this extension by an abelian extension over $L/ K$ to $L_{\infty}$. Let $M$ be the maximal $p$-abelian $p_1$-ramified 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 extensions. Part of this talk is joint work with Vlad Crisan.

number theory

Audience: researchers in the discipline


POINT: New Developments in Number Theory

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Organizers: Jessica Fintzen*, Karol Koziol*, Joshua Males*, Aaron Pollack, Manami Roy*, Soumya Sankar*, Ananth Shankar*, Vaidehee Thatte*, Charlotte Ure*
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