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Preprint (Vorabdruck) zugänglich unter
Anderson's double complex and gamma monomials for rational function fields
URN: urn:nbn:de:bsz:291-scidok-43363
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4336/
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Dokument 1.pdf (403 KB)
Institut:
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität 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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