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I could not find a reference of the local version of Weierstrass preparation theorem It is used for example in Denef & van den Dries "$p$-adic and real subanalytic sets". Can you help, thank you

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up vote 3 down vote accepted

See '$p$-adic numbers, $p$-adic analysis, and zeta-functions' by Koblitz. Chapter IV sections 3 and 4 have a good exposition on newton polygons and the Weierstrass preparation theorem.

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Thank you for your help. – user17090 Oct 1 '11 at 15:04
What I need more precisely is the statment and proof of LOCAL weierstrass preparation. I did not find that in Koblitz's book. – user17090 Oct 10 '11 at 16:46

A good elementary proof of the Weierstrass preparation theorem can be found in the Jun-ichi Igusa's An introduction to the theory of Local Zeta Functions (Google books link).

See Chapter 2, section 2.3.

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