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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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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 book of Jun-ichi Igusa

An introduction to the theory of Local Zeta Functions http://books.google.com.mx/books/about/An_Introduction_to_the_Theory_of_Local_Z.html?id=yPXK10jqMj8C&redir_esc=y

See Chapter 2, section 2.3.

Hope to help.

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