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Transactions of the American Mathematical Society

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Anderson's double complex and gamma monomials for rational function fields


Authors: Sunghan Bae, Ernst-Ulrich Gekeler, Pyung-Lyun Kang and Linsheng Yin
Journal: Trans. Amer. Math. Soc. 355 (2003), 3463-3474
MSC (2000): Primary 11R58
DOI: https://doi.org/10.1090/S0002-9947-03-03288-4
Published electronically: May 29, 2003
MathSciNet review: 1990158
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Abstract: We investigate algebraic $\Gamma $-monomials of Thakur's positive characteristic $\Gamma $-function, by using Anderson and Das' double complex method of computing the sign cohomology of the universal ordinary distribution. We prove that the $\Gamma $-monomial associated to an element of the second sign cohomology of the universal ordinary distribution of $\mathbb{F} _{q}(T)$generates a Kummer extension of some Carlitz cyclotomic function field, which is also a Galois extension of the base field $\mathbb{F} _{q}(T)$. These results are characteristic-$p$ analogues of those of Deligne on classical $\Gamma $-monomials, proofs of which were given by Das using the double complex method. In this paper, we also obtain some results on $e$-monomials of Carlitz's exponential function.


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Additional Information

Sunghan Bae
Affiliation: Department of Mathematics, KAIST, Taejon 305-701, Korea
Email: shbae@math.kaist.ac.kr

Ernst-Ulrich Gekeler
Affiliation: Department of Mathematics, Saarland University, D-66041 Saarbrucken, Germany
Email: gekeler@math.uni-sb.de

Pyung-Lyun Kang
Affiliation: Department of Mathematics, Chungnam National University, Taejon 305-764, Korea
Email: plkang@math.cnu.ac.kr

Linsheng Yin
Affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China
Email: lsyin@math.tsinghua.edu.cn

DOI: https://doi.org/10.1090/S0002-9947-03-03288-4
Received by editor(s): March 12, 2001
Published electronically: May 29, 2003
Additional Notes: The first author was supported by KOSEF cooperative Research Fund and DFG
The fourth author was supported by Distinguished Young Grant in China and a fund from Tsinghua
Article copyright: © Copyright 2003 American Mathematical Society

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