Geodesic
About the algebraic closure of the field of power series in several variables in characteristic zero
Journal of Singularities, Tome 16 (2017), pp. 1-51

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We begin this paper by constructing different algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields depends on the choice of an Abhyankar valuation and is constructed via a generalization of the Newton-Puiseux method for this valuation.
DOI : 10.5427/jsing.2017.16a
Classification : :13F25.:11J25, 12J20, 12F99, 13J05, 14B05, 32B10. 
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     author = {Guillaume Rond},
     title = {About the algebraic closure of the field of power series in several variables in characteristic zero},
     journal = {Journal of Singularities},
     pages = {1--51},
     publisher = {mathdoc},
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     year = {2017},
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     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2017.16a/}
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Guillaume Rond. About the algebraic closure of the field of power series in several variables in characteristic zero. Journal of Singularities, Tome 16 (2017), pp. 1-51. doi: 10.5427/jsing.2017.16a

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