Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt
2020 Manuscripta mathematica  
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. Mathematics Subject Classification: 11G15 · 11G30 · 12F12
doi:10.1007/s00229-020-01213-2 fatcat:vjb6fx655vhtbdcr2w5bwdhzmi