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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

Zap. Nauchn. Sem. POMI, 2005 Volume 321, Pages 13–35 (Mi znsl406)

On semicontinuity of ramification invariants in dimension 2

O. Yu. Vanushina

Saint-Petersburg State University

Abstract: 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.

UDC: 512

Received: 01.10.2004


 English version:
Journal of Mathematical Sciences (New York), 2006, 136:3, 3837–3849

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