Title: Adeles and Differential Forms (with R. Hübl)
Publication status: appeared in J. reine angew. Math. 471 (1996), 1-22
The relation between Beilinson's scheme theoretic adeles on a scheme X, and the Grothendieck residue complex of X, is examined. We show that there is an explicit map the adeles to the residue complex, which is given by "taking residues." The existence of such a map was predicted by J. Lipman.
We also show that the adeles can be used to resolve the De Rham complex, thus computing the algebraic De Rham cohomology of X.
updated 26 Jan 2012