Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt

doi:10.1007/s00229-020-01213-2

Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt

School of Mathematics

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Abstract

Fix a positive integer g and rational prime p. We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is tame by imposing conditions on the endomorphism ring. As an application, we consider the tame inverse Galois problem and are able to realise general symplectic groups as Galois groups of tame extensions of Q.

Original language	English
Pages (from-to)	283-290
Journal	Manuscripta Mathematica
Volume	165
Issue number	1
DOIs	https://doi.org/10.1007/s00229-020-01213-2
Publication status	Published - 3 Jun 2020

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AB - Fix a positive integer g and rational prime p. We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is tame by imposing conditions on the endomorphism ring. As an application, we consider the tame inverse Galois problem and are able to realise general symplectic groups as Galois groups of tame extensions of Q.

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Tame torsion, the tame inverse Galois problem, and endomorphisms

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