Title: The Action of Adeles on the Residue Complex
Publication status: Communications in Algebra Volume 31, Issue 8, 2003 (special Steven Kleiman issue)
Abstract:
Let X be a scheme of finite type over a
perfect field k. In this paper we study the relation between two
important objects associated to X: the Grothendieck residue complex
and the Beilinson adeles complex. It is known that the complex of
adeles is a DGA (differential graded algebra). Our first main result
is that the residue complex is a right DG module over the adeles
complex. The second main result is that the de Rham residue complex
is a DG module over the de Rham adeles complex. This action gives
rise to the cap product in de Rham (co)homology.
Electronic Preprint: LaTeX , postscript . See also eprint at arXiv: math.AG/0205018
Paper in journal (full text requires access permission)
(updated: 20 Apr 2013)