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The function field analog of the theorem of Mazur-Kamienny-Merel (giving a universal bound in $[K:\mathbb{Q}]$ for the size of the $K$-rational torsion of an elliptic curve) is immediate just from the ...

This is one of the theorems in Field Arithmetic written by M. Fried and M. Jarden as following which is Proposition 13.4.6 in that monograph: Every field K has a regular extension F which is PAC ...