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Preprint (Vorabdruck) zugänglich unter
URN: urn:nbn:de:bsz:291-scidok-43363
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4336/


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

Bae, Sunghan ; Gekeler, Ernst-Ulrich ; Kang, Pyung-Lyun ; Yin, Linsheng

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Institut: Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe: Mathematik
Dokumentart: Preprint (Vorabdruck)
Schriftenreihe: Preprint / Fachrichtung Mathematik, Universit├Ąt des Saarlandes
Bandnummer: 28
Sprache: Englisch
Erstellungsjahr: 2001
Publikationsdatum: 22.11.2011
Kurzfassung auf Englisch: We investigate algebraic \Gamma-monomials of Thakur's positive characteristic \Gamma-function, by using Anderson-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 the 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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