SKETCH OF A PROGRAMME

SKETCH OF A PROGRAMME
by Alexandre Grothendieck

1. As the present situation makes the prospect of teaching at the research
level at the University seem more and more illusory, I have resolved to apply
for admission to the CNRS, in order to devote my energy to the development
of projects and perspectives for which it is becoming clear that no student
(nor even, it seems, any mathematical colleague) will be found to develop
them in my stead.
In the role of the document “Titles and Articles”, one can find after this
text the complete reproduction of a sketch, by themes, of what I considered
to be my principal mathematical contributions at the time of writing that
report, in 1972. It also contains a list of articles published at that date. I
ceased all publication of scientific articles in 1970. In the following lines,
I propose to give a view of at least some of the principal themes of my
mathematical reflections since then. These reflections materialised over the
years in the form of two voluminous boxes of handwritten notes, doubtless
difficult to decipher for anyone but myself, and which, after several successive
stages of settling, are perhaps waiting for their moment to be written
up together at least in a temporary fashion, for the benefit of the mathematical
community. The term “written up” is somewhat incorrect here, since
in fact it is much more a question of developing the ideas and the multiple
visions begun during these last twelve years, to make them more precise and
deeper, with all the unexpected rebounds which constantly accompany this
kind of work – a work of discovery, thus, and not of compilation of piously
accumulated notes. And in writing the “Mathematical Reflections”, begun
since February 1983, I do intend throughout its pages to clearly reveal the
process of thought, which feels and discovers, often blindly in the shadows,
with sudden flashes of light 1 when some tenacious false or simply inadequate
2 image is finally shown for what it is, and things which seemed all crooked
fall into place, with that mutual harmony which is their own.

In any case, the following sketch of some themes of reflection from the
last ten or twelve years will also serve as a sketch of my programme of work
for the coming years, which I intend to devote to the development of these
themes, or at least some of them. It is intended on the one hand for my
colleagues of the National Committee whose job it is to decide the fate of
my application, and on the other hand for some other colleagues, former
students, friends, in the possibility that some of the ideas sketched here
might interest one of them.