Andersons double complex and gamma monomials for rational function fields

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 F-q( T) generates a Kummer extension of some Carlitz cyclotomic function field, which is also a Galois extension of the base field 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.