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Have added more of the original (“historical”) References with brief comments and further pointers.
added a lightning quick paragraph at Properties – GAGA on a sufficient condition for a complex-analytic Deligne cocycle to lift to a complex algebraic one. (Thanks to David Roberts for the pointer!)
Added the reference
which introduces an interesting generalization of Deligne cohomology, by reformulating it via simplicial presheaves.
I also started some notes at Higher regulators and values of L-functions but didn’t get very far yet.
I have expanded a good bit the Idea section.
I am spelling out details at Deligne cohomology in the expository style (or at least that’s the intention) of geometry of physics. So far there is now a section Definition – In smooth differential geometry.
Wrote a section Characteristic maps out of and into Deligne cohomology spelling out the construction of all the relevant maps (curvatue, underlying class etc.) as zig-zags of chain maps. From this will nicely follow all the exactness yoga, which I am now writing out in the next section.
Wrote a section Deligne cohomology – Porperties – Chern character which spells out how the Deligne complex is the homotopy pullback of closed differential forms along the “higher abelian Chern character” map.
(All this has been at circle n-bundle with connection for a long time, but, looking back now, this looks quite messy, whereas the new version now should be much more readable. I hope.)
Wrote a section Deligne cohomology – Properties – The exact sequences for curvature and characteristic classes which spells out the proof of the curvature and characteristic class short exact sequence as it follows naturally from the above homotopy pullback characterization.
Wrote a section Deligne cohomology – Properties – The exact differential cohomology hexagon concluding the above discussions.
Did a little more polishing at Deligne cohomology, rearranged the sub-sections slightly to flow more naturally. Copied the definition of Cech hypercohomology over to the subsection on Preliminaries on sheaf cohomology in order to be a tad more self-contained.
added a more illustrative picture of the Cech-Deligne double complex here
added publication data for the English translation of:
Alexander Beilinson, Higher regulators and values of L-functions, Journal of Soviet Mathematics 30 (1985), 2036-2070, (mathnet (Russian), DOI)
English translation: J Math Sci 30, 2036–2070 (1985) (doi:10.1007/BF02105861)
I have added ISBN:978-0-12-581120-0 to
but something strange is going on: the webpage claims that strictly all contributions to the book have been WITHDRAWN (in capitals) including the Front Matter, the Copyright statement and the Preface.
I suppose this is a glitch of the “publisher”’s computer system?
It’s not a glitch, if you download a PDF, it explains the withdrawal:
This article has been withdrawn: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy). This Book/Chapter has been as the rights have been returned to the author.
I saw that. But how is that an explanation? It just says “withdrawn” in more words, no?
Apart from the dubious idea that there is anything to withdraw from a book in print (not a journal), what makes it look like a computer glitch is that every single item of this book is marked as withdrawn, even pieces that have not been submitted by anyone, such as the copyright statement, and the title page. That makes no sense.
I mean, the page claims that the very invitation to a conference that did take place, and did so 32 years ago, has been… withdrawn.
You can tell that Elsevier’s webpages for the scientific literature they are selling are autogenerated, with little to no human intervention. The other day I came across pages selling Connections, Curvature, and Cohomology which had title and author names mutilated, evidently caused by failing OCR.
Let’s just say I’m not surprised by Elsevier’s bad quality here. Their scans of old articles from eg JPAA are atrocious. Not to mention they are a money-making machine, not our friend. I suspect Elsevier just has an automated system that couldn’t cope with someone exercising their author’s rights and so it just nuked the whole volume.
I’ve seen issues of old things from Springer not available electronically because of rights issues before, so that’s not totally peculiar. And, if I were Esnault et al I would be putting the book up for free on the internet, as opposed to letting Elsevier charge people for it.
Added Ahem, see #19 below
For what it’s worth Rapoport’s contribution is here. Maybe we could track down as many papers from the volume are freely available and link to them from a page for the whole book?
Or….. see this page! :-D
I still think we should have a page for the book, with links for each of the papers, since I think an nLab page would turn up a lot higher in Google’s search algorithms than that well-hidden and partly-broken personal webpage. And, ideally, would compete with the completely useless Elsevier page for the book.
Go ahead! :-)
What happened is that the rights were returned to the authors because the book is out of print. Older copyright agreements often contain such a provision.
I created the page Beilinson’s Conjectures on Special Values of L-Functions.
So you think the nature of that webpage is intentional? Hm, okay, strange.
And the nLab page for the book gets a high-up first page hit on Google search results :-) (checked it in an anonymous window)
Yeah, that’s why it’s important to cross-link nLab entries after creating them.
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