The Grimoire is a textbook on commutative algebra
for advanced master students and graduate students that
I am currently writing. Some of its last chapters could
be interesting also to more advanced researchers. It is
written in French. Here you can download the current version :

Your comments are welcome and gratefully acknowledged!

Status Update :

November 8, 2014 : work on the Grimoire project
has resumed. Lectures
Bélier, Taureau et Gémeaux are complete; currently
working on Cancer.

December 7, 2014 : Lectures
Bélier, Taureau, Gémeaux et Cancer are complete;
currently working on Lion.

March 6, 2015 : Lectures
Bélier, Taureau, Gémeaux, Cancer and Lion are complete;
currently working on Vierge.

May 23, 2015 : The Grimoire Project enters Summer recess : until
the end of September I will be working on a different project,
so there will be not much action for the Grimoire : I might make
the occasional correction, and maybe toy with the index once and
then, but other than that don't expect much until October.
The Vierge lecture is not quite
finished yet, but it is well advanced.

October 14, 2015 : work on the Grimoire project has resumed.
Currently working on Vierge.

October 23, 2015 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion et Vierge are complete;
currently working on Balance.

November 1, 2015 : I've corrected the proof of Zariski's Main Theorem,
that was confusing and slightly broken in various places. Please
download the revised version, and keep on sending me your remarks.
I've also added a result on UFDs with some applications, at the end
of section 11.4. Now, back to Balance.

December 15, 2015 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge and Balance
are complete; currently working on Scorpion.
I've also made some small corrections to the proof of Swan's theorem
in Lecture 5 (Lion), and I've added some
exercices at the end of section 6.5.

February 1, 2016 : I've taken the important decision to add
a section (a revised section 5.5 that I'm writing now) on the
language of sheaves and a few basic notions of scheme theory.
This has entailed some reorganization in lectures
Lion, Vierge and Balance.
The reason to include this material is that eventually I'm planning
to give a presentation of a valuation-theoretic proof due (essentially)
to Fujiwara of Gruson-Raynaud's important theorem on flattening of
morphisms by admissible blow-ups. This proof is more elementary
than Gruson and Raynaud's original argument, but of course to
properly state the theorem and to give a clean presentation
of its proof it is convenient to be able to manipulate some
non-affine schemes (such as blow-ups).

April 7, 2016 : I've finally completed the digression on
sheaves and schemes announced in February; it is longer
than originally planned and is now split over two
sections : the new section 3.4 on sheaves and the new
section 5.5 on schemes. This entailed some rearranging
of material around the text. Now I'm ready to return to
Scorpion.

April 29, 2016 : The Grimoire Project enters Summer recess : until
late September I will be working on a different project, so not
much will happen on this page. Scorpion
is not quite finished, but is well advanced. See you in a few months!

November 21, 2016 : The Grimoire Project is active again!
I was very busy until now, but at last I am free. I've just
started a new section in Scorpion,
dedicated to the real spectrum of a ring : it doesn't contain
much at present, but watch it grow!

January 16, 2017 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge, Balance and
Scorpion are complete; next up is
Sagittaire.

April 13, 2017 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge, Balance,
Scorpion and Sagittaire are complete. I've also
made several minor fixes in earlier parts of the text, and
added several new entries to the index.
There will be a few further updates next week, then
the Grimoire Project will enter Summer recess.

December 12, 2017 : work on the Grimoire Project has
finally resumed! Currently working on
Capricorne.

March 4, 2018 : today the Grimoire Project has reached
an important milestone : the proofs of both the Gruson-Raynaud
theorem and of elimination of quantifiers for fields with
non trivial valuations are complete : see theorems 10.57
and 10.62 (I give a geometric form of elimination of
quantifiers : see the remarks before paragraph 10.4.3).
Still working on Capricorne :
section 4 is almost done, and it remains (only) to write section 5.

Mai 5, 2018 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge, Balance,
Scorpion, Sagittaire and Capricorne are complete. Today the
Grimoire also enters officially into summer recess. I
might do some little cleaning up, and also add a few entries
to the index, but that will be it until October at the
earliest, I expect.

June 27, 2018 : I took advantage of some free time to make a
thorough reorganization of the last 4 chapters of the Grimoire
(and I've also added an exercise in what is now section 9.2).
The upshot is that, for the time being, the Grimoire is complete
only up to Sagittaire, so in a sense
this is a step backward, but it's only in order to prepare a leap
forward that I'll take after the summer : then hopefully I'll be
able to complete both Capricorne and
Verseau in a relatively short time.
Also, you can start seeing now the general shape that
Poissons will have in the end : more
material is planned, but the basic scaffolding is in place.

September 23, 2018 : work on the Grimoire Project has resumed!
Currently working on the revised version of
Capricorne.

November 2, 2018 : I'm finally done with the revision of
Capricorne! It took slightly
longer and slightly more effort than I had anticipated,
because while working on it, I realized that the previous draft
was rather (and embarassingly) rough : now it is much better.
Hence : lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge, Balance,
Scorpion, Sagittaire and Capricorne are again complete,
and I'll start working on Verseau
in a matter of days, after I rest a little bit with a short break.

December 30, 2018 : During the holidays I'm not working on
Verseau, but I'm not quite idle
either : I just finished fixing a very old and embarrassing
mistake : the homological and cohomological notations for
complexes were all mixed up, throughout the Grimoire. I have
been aware of the problem for years, but I had never found the
time and the nerve to correct this : now it's done. I'll resume
working on Verseau around the
second week of January : stay tuned!

January 26, 2019 : Lectures
Bélier, Taureau, Gémeaux, Cancer, Lion, Vierge, Balance,
Scorpion, Sagittaire, Capricorne and Verseau are
complete. I'm taking a well deserved break from the Grimoire,
to take care of a bunch of long-delayed other smaller projects.

April 22, 2019 : I've just completed a major revision of
Bélier : two of the previous
sections (1.3 and 1.4) have fused into a single longer
one, and a new section 1.4 has been added, containing a
self-contained treatment of the elementary theory of fields;
moreover, some material on unique factorisation domains has
been moved from section 5.2 to section 1.1.