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 | References | Similar Articles | Additional Information

Abstract: We investigate algebraic -monomials of Thakur's positive characteristic -function, by using Anderson and Das' double complex method of computing the sign cohomology of the universal ordinary distribution. We prove that the -monomial associated to an element of the second sign cohomology of the universal ordinary distribution of generates a Kummer extension of some Carlitz cyclotomic function field, which is also a Galois extension of the base field . These results are characteristic- analogues of those of Deligne on classical -monomials, proofs of which were given by Das using the double complex method. In this paper, we also obtain some results on -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