The ring of polynomial functors of prime degree
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Abstract:
Let $\hat {\mathbb {Z}}_p$ be the ring of $p$-adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to $\hat {\mathbb {Z}}_p$-modules of degree at most $p$ is equivalent to the category of modules over a particularly well understood ring, called Green order. This case was conjectured by Yuri Drozd.References
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Additional Information
- Alexander Zimmermann
- Affiliation: Département de Mathématiques et CNRS UMR 7352, Université de Picardie, 33 rue St Leu, F-80039 Amiens Cedex 1, France
- MR Author ID: 326742
- Email: alexander.zimmermann@u-picardie.fr
- Received by editor(s): April 17, 2013
- Received by editor(s) in revised form: July 29, 2013, and August 12, 2013
- Published electronically: December 17, 2014
- Additional Notes: This research was supported by a grant “PAI alliance” from the Ministère des Affaires Étrangères de France and the British Council. The author acknowledges support from STIC Asie of the Ministère des Affaires Étrangères de France
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 367 (2015), 7161-7192
- MSC (2010): Primary 16H10; Secondary 20C30, 20J06, 55R40
- DOI: https://doi.org/10.1090/S0002-9947-2014-06265-X
- MathSciNet review: 3378827