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An existential 0-definition of F_q[[t]] in F_q((t))

Abstract:

We show that the valuation ring F_q[[t]] in the local field F_q((t)) is existentially definable in the language of rings with no parameters. The method is to use the definition of the henselian topology following the work of Prestel-Ziegler to give an existential-F_q-definable bounded neighbouhood of 0. Then we `tweak' this set by subtracting, taking roots, and applying Hensel's Lemma in order to find an existential-F_q-definable subset of F_q[[t]] which contains tF_q[[t]]. Finally, we use th...

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publication date:
2013-06-28
Keywords:
Pubs id:
pubs:414384
UUID:
uuid:6a78412e-6d88-4cbe-82db-65edd6cb7e3b
Local pid:
pubs:414384
Source identifiers:
414384
Deposit date:
2013-11-17

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