Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Defect of an extension, key polynomials and local uniformization   For all simple and finite extension of a valued field, we prove that its
defect is the product of the effective degrees of the complete set of key
polynomials associated. As a consequence, we obtain a local uniformization
theorem for valuations of rank 1 centered on an equicharacteristic
quasi-excellent local domain satisfying some inductive assumptions of lack of
defect.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th