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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Algebraic independence of periods and logarithms of Drinfeld modules


Authors: Chieh-Yu Chang and Matthew A. Papanikolas; with an appendix by Brian Conrad
Journal: J. Amer. Math. Soc. 25 (2012), 123-150
MSC (2010): Primary 11J93; Secondary 11G09, 11J89
Published electronically: August 1, 2011
MathSciNet review: 2833480
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Abstract: Let $ \rho$ be a Drinfeld $ A$-module with generic characteristic defined over an algebraic function field. We prove that all of the algebraic relations among periods, quasi-periods, and logarithms of algebraic points on $ \rho$ are those coming from linear relations induced by endomorphisms of $ \rho$.


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Additional Information

Chieh-Yu Chang
Affiliation: Department of Mathematics, National Tsing Hua University, No. 101, Sec. 2, Kuang Fu Road, Hsinchu City 30042, Taiwan, Republic of China and National Center for Theoretical Sciences, Hsinchu City 30042, Taiwan, Republic of China
Email: cychang@math.cts.nthu.edu.tw

Matthew A. Papanikolas
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843 U.S.A.
Email: map@math.tamu.edu

Brian Conrad
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305 U.S.A.
Email: conrad@math.stanford.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2011-00714-5
PII: S 0894-0347(2011)00714-5
Keywords: Algebraic independence, Drinfeld modules, periods, logarithms
Received by editor(s): May 27, 2010
Received by editor(s) in revised form: May 23, 2011
Published electronically: August 1, 2011
Additional Notes: The first author was supported by an NCTS postdoctoral fellowship.
The second author was supported by NSF Grant DMS-0903838.
The author of the appendix was supported by NSF grant DMS-0917686.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.