NT seminar tomorrow (Tuesday): Asimina Hamakiotes (UConn)
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Bianca Viray
Jan 22, 2024, 11:44:04 PMJan 22
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Hi everyone,
Our first seminar of the quarter is tomorrow at 11am in Padelford C-401. Title and abstract are below. We will go to lunch with the speaker after the talk, and students will be subsidized. See you tomorrow!
Title: Elliptic curves with complex multiplication and abelian division fields
Abstract: Let $K$ be an imaginary quadratic field, and let $\mathcal{O}_{K,f}$ be an order in $K$ of conductor $f \geq 1$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_{K,f}$, such that $E$ is defined by a model over $\mathbb{Q}(j_{K,f})$, where $j_{K,f} = j(E)$. Let $N \geq 2$ be an integer. In this talk, we will see when $\mathbb{Q}(j_{K,f},E[N])$ is an abelian extension of $\mathbb{Q}(j_{K,f})$. Further, when the extension $\mathbb{Q}(j_{K,f},E[N])/\mathbb{Q}(j_{K,f})$ is not abelian, we will discuss what the possible maximal abelian subextensions are.
Abstract: Let $K$ be an imaginary quadratic field, and let $\mathcal{O}_{K,f}$ be an order in $K$ of conductor $f \geq 1$. Let $E$ be an elliptic curve with complex multiplication by $\mathcal{O}_{K,f}$, such that $E$ is defined by a model over $\mathbb{Q}(j_{K,f})$, where $j_{K,f} = j(E)$. Let $N \geq 2$ be an integer. In this talk, we will see when $\mathbb{Q}(j_{K,f},E[N])$ is an abelian extension of $\mathbb{Q}(j_{K,f})$. Further, when the extension $\mathbb{Q}(j_{K,f},E[N])/\mathbb{Q}(j_{K,f})$ is not abelian, we will discuss what the possible maximal abelian subextensions are.
Bianca Viray (she/her)
Craig McKibben and Sarah Merner Professor of Mathematics
University of Washington
Seattle, WA 98195
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