Anderson’s double complex and gamma monomials for rational function fields
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- by Sunghan Bae, Ernst-Ulrich Gekeler, Pyung-Lyun Kang and Linsheng Yin PDF
- Trans. Amer. Math. Soc. 355 (2003), 3463-3474 Request permission
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.References
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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
- 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 - © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 3463-3474
- MSC (2000): Primary 11R58
- DOI: https://doi.org/10.1090/S0002-9947-03-03288-4
- MathSciNet review: 1990158