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- W2767029376 abstract "We prove structure theorems for the moduli stack of elliptic curves equipped with $G$-structures, where $G$ is a finite 2-generated metabelian group. In particular, we show that if $G$ has exponent $e$, then there is a subgroup $Hle GL_2(mathbb{Z}/e)$ such that $G$-structures on elliptic curves $E$ are equivalent to congruence structures of level $H$. Our methods are almost entirely group theoretic. Let $widehat{M}$ denote the free profinite metabelian group of rank 2, then along the way we prove a decomposition of $Out(widehat{M})$ as an internal semi-direct product of the subgroup of braid-like outer with the subgroup of IA outer automorphisms which induce the identity on the abelianization. We also show a surprising result that all IA-automorphisms leave every open normal subgroup stable." @default.
- W2767029376 created "2017-11-10" @default.
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- W2767029376 date "2017-10-16" @default.
- W2767029376 modified "2023-09-26" @default.
- W2767029376 title "Arithmetic monodromy actions on pro-metabelian fundamental groups of once-punctured elliptic curves" @default.
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- W2767029376 hasPublicationYear "2017" @default.
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