In the last 2 decades a method of constructing algebraic objects over semi-global fields (one-variable function fields over complete discretely valued fields) by patching together compatible objects constructed on a network of field extensions has been introduced and developed by Harbater, Hartmann, and Krashen. Field patching has proven to be a powerful tool in considering the problem of admissibility over these fields. Given a finite group G and a field F we say that G is admissible over F if there is a division algebra central over F with a maximal subfield that is a Galois extension of F with group G. Fixing a field F, we can ask, which groups are admissible over F? I will present a recent result which completely solves the admissibility problem for a class of semi-global fields (equicharacteristic with algebraically closed residue fields) using field patching techniques and results from generic Galois theory.
Galois Extensions in Division Algebras Over Semi-Global Fields
Yael Davidov, University of DelawareAuthors: Yael Davidov
2023 AWM Research Symposium
Combinatorial and Homological Methods in Commutative Algebra [Organized by Francesca Gandini and Selvi Kara]