A bicategorical version of Masuoka's theorem. Applications to bimodules over functor categories and to firm bimodules

Details A bicategorical version of Masuoka's theorem. Applications to bimodules over functor categories and to firm bimodules A bicategorical version of Masuoka's theorem. Applications to bimodules over functor categories and to firm bimodules

2008-08-19

arxiv.org/abs/0808.2553v1

Mathematics

Rings and Algebras

Scientific paper

We give a bicategorical version of the main result of A. Masuoka ({Corings and invertible bimodules,} {\em Tsukuba J. Math.} \textbf{13} (1989), 353--362) which proposes a non-commutative version of the fact that for a faithfully flat extension of commutative rings $R \subseteq S$, the relative Picard group $Pic(S/R)$ is isomorphic to the Amitsur 1--cohomology group $H^1(S/R,U)$ with coefficients in the units functor $U$.

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