Geodesic
Classification of convergence sets of multidimensional complete fields
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 117-126

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Convergence sets of a multidimensional complete field (that is, such that all power series above them converge when substituting an element of the maximal ideal instead of a variable) are classified by inclusion in some standard convergence ring. In addition, an algorithm for constructing this ring is given. 
@article{ZNSL_2024_531_a6,
     author = {A. I. Madunts},
     title = {Classification of convergence sets of multidimensional complete fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {117--126},
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     volume = {531},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a6/}
}
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A. I. Madunts. Classification of convergence sets of multidimensional complete fields. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 40, Tome 531 (2024), pp. 117-126. http://geodesic.mathdoc.fr/item/ZNSL_2024_531_a6/