Compositions of consistent systems of rank one discrete valuation rings

Details Compositions of consistent systems of rank one discrete valuation rings Compositions of consistent systems of rank one discrete valuation rings

2008-09-26

arxiv.org/abs/0809.4525v1

Mathematics

Commutative Algebra

31 pages

Scientific paper

Let V be a rank one discrete valuation ring (DVR) on a field F and let L/F be a finite separable algebraic field extension with [L:F] = m. The integral closure of V in L is a Dedekind domain that encodes the following invariants: (i) the number of extensions of V to a valuation ring W on L, (ii) the residue degree of each W over V, and (iii) the ramification degree of each W over V. Given a finite set of DVRs on F, an m-consistent system is a family of sets enumerating what is theoretically possible for the above invariants of each V in the set. The m-consistent system is realizable if there exists a finite separable extension field L/F that gives for each V the listed invariants. We investigate the realizability of m-consistent systems.

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