Geodesic
On semicontinuity of ramification
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 13-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a cyclic extension $L/K$ of field $K=k[[T,U]]$ of characteristic $2$. It is shown, for all sufficiently large $N$, jets of order $N$ of all curves, which are not components of ramification locus, for which the corresponding valuation of the function field has the unique extension, valuations of coefficients of equation of Inaba are positive, and ramification jumps are maximal is open set. In the case of a general (not cyclic) extension, it is shown that the set of jets with the fixed value of $k$th jump is an intersection of open and close sets. 
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O. Yu. Vanushina. On semicontinuity of ramification. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 12, Tome 321 (2005), pp. 13-35. http://geodesic.mathdoc.fr/item/ZNSL_2005_321_a1/

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[3] J.-P. Serre, Local Fields, Springer-Verlag, New-York, 1979 | MR

[4] E. Inaba, “On matrix equations for Galois extensions of fields with characteristic $p$”, Natural Science Report Ochanomizu University, 12:2 (1961), 26–35 | MR