These days I found a mysterious [page on Google books](https://books.google.com.br/books/about/On_the_De_Rham_cohomology_of_schemes.html?id=plrvAAAAMAAJ&redir_esc=y) describing a book entitled *On the De Rham cohomology of schemes* by Grothendieck, Coates, and Jussila.


At once I thought this was an error and Google books had miss-indexed Exposé IX of Dix Exposés sur la Cohomologie de Schémas. However, the references diverge both in their titles:



> 
> **Crystals and the De Rham Cohomology of Schemes**
> 
> 
> vs.
> 
> 
> **On the De Rham cohomology of schemes**,
> 
> 
> 


as well as their numbers of pages (53 in Dix Exposés vs. 106 in this reference).


The book is even cited in [Cisinski 's Habilitation thesis](https://www.math.univ-toulouse.fr/~dcisinsk/hab.pdf) as



> 
> [Gro66] A. Grothendieck « On the de Rham cohomology of schemes » Publ. Math. IHES **29** (1966), p. 93--103.
> 
> 
> 


Maybe this is "On the de Rham cohomology of algebraic varieties", but again, the references diverge in page number and title.


So, does this book really exists, and, if so, is it available anywhere?



On a mysterious reference of Grothendieck
I think your hunch is correct that Google is in error, and that "Crystals and the de Rham cohomology of schemes" refers to the article in Dix Exposés. I doubt there is a book by the same name and author. There is also "On the de Rham cohomology of algebraic varieties" but that's different. The first is a long proposal for crystalline cohomology (which hadn't been developed at that point), and the second is an extract from a letter to Atiyah giving a proof of the algebraic de Rham theorem. Does that help?


