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On a theory of the b-function in positive characteristic

Abstract:

We present a theory of the $b$-function (or Bernstein–Sato polynomial) in positive characteristic. Let $f$ be a non-constant polynomial with coefficients in a perfect field $k$ of characteristic $p>0$. Its $b$-function $b_f$ is defined to be an ideal of the algebra of continuous $k$-valued functions on $Z_p$. The zero-locus of the $b$-function is thus naturally interpreted as a subset of $Z_p$, which we call the set of roots of $b_f$. We prove that bf has finitely many roots and that...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1007/s00029-017-0383-x

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Publisher:
Springer Verlag Publisher's website
Journal:
Selecta Mathematica Journal website
Publication date:
2018-02-02
Acceptance date:
2017-12-12
DOI:
EISSN:
1420-9020
ISSN:
1022-1824
Pubs id:
pubs:828239
URN:
uri:27a33b4f-1c63-44e7-a6b8-759980a015ad
UUID:
uuid:27a33b4f-1c63-44e7-a6b8-759980a015ad
Local pid:
pubs:828239

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