Kummer theory for function fields

Félix Baril Boudreau; Antonella Perucca

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arXiv · 2407.10783

Kummer theory for function fields

Félix Baril Boudreau·Antonella Perucca

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Abstract

We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the structure of its Galois group. Our results show in a precise sense how the questions of computing the degrees of these extensions and of computing the group structures of their Galois groups reduce to the corresponding questions for the Kummer extensions of their constant fields.

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Félix Baril Boudreau, Antonella Perucca. 2024-07-15. Kummer theory for function fields. https://arxiv.org/abs/2407.10783

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