In the Promenade, and here and there in Récoltes et Semailles I will be .. travaux mathematiques de A. Grothendieck”)was written in in. Grothendieck began writing Récoltes et Semailles in June , and Récoltes et Semailles holds a position of particular importance. Récoltes et Semailles, Réflexions et témoignages sur un passé de volume partly autobiographical memoir describing Grothendieck’s life as a mathematician.

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I wouldn’t quite put matters the way you did, but I have no real objection to that formulation either. However, I recall for instance reading Grothendieck’s opinion that standard conjectures were false, and claiming he had in mind a few related conjectures which he doesn’t state precisely which might turn out to be the right ones. Would it be ok to say that the motive of anabelian studies is to see, how far “arithmetics” and “topology” coincide?

Catalin marked it as to-read Jan 12, One suspects that the habits of the Grothendieck school, whereby the six operations had to be established first in every situation where a problem seemed worth solving, could be enormously helpful in some situations, and limiting in some others. Joie added it Jul 01, And the hierarchy goes on I am still not sure I interpret you question correctly, so I will refrain from editing it myself.

If this is the case, I’d appreciate a reference. More precisely, motives were inadequate for the study of points the most basic maps between schemes!


But the transfer results between tame theories that are sketched in “Esquisse” are not really there yet, and I’m not sure if it’s because it’s too early or because it’s not really what researchers in the field are after.

Return to Book Page. Even though I wasn’t knowledgeable enough to have an opinion about the social commentary in the book, I did wonder quite a bit if some of the discontent could have a purely mathematical source. As for “tame topology” my impression is that he topic has not taken off, but I may be wrong about this. Michel rated it really liked it Nov 14, Lists with This Book.

Alexandre Grothendieck: Récoltes et semailles ()

grthendieck Nicolas Delporte marked it as to-read Dec 18, A clue came shortly afterwards, when I heard from Faltings Grothendieck’s ideas on anabelian geometry.

Andrius Kulikauskas 80 8.

For a bit of an update, see my paper with Coates grothnedieck. It has been translated to some languages other than English, but I do not know about an English version.

For a specialist in PDEs, certainly the answer is a resounding no. Post as a guest Name. I’m glad you enjoyed it.

Récoltes et semailles: Réflexions et témoignage sur un passé de mathématicien.

It seems to me that this line of research has not been pursued, mainly for two reasons. He is noted for his mastery of abstract approaches to mathematics, and his perfectionism in matters of formulation and presentation.

In particular, he demonstrated the ability to derive concrete results using only very general methods. The ideas were already outdated or have been proven wrong.

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To summarize, I’m suggesting that the mathematical content of Grothendieck’s strong objection to motives was inextricably e with his ideas on homotopy theory as appeared in ‘Pursuing Stacks’ and the anabelian letter to Faltings, and catalyzed by his realization that the motivic philosophy had been of limited use maybe even a bit of an obstruction in the proof of the Mordell conjecture. There is a translation into Russian.

Cook 13k 2 28 Mathematics Stack Exchange works best with JavaScript enabled. At least it made Grothendieck’s “Esquisse d’un programme” more visible and it is clear that the topics there like anabelian geometry or the new foundations for homotopical algebra have been two avenues of research of great interest recently.

Tecoltes still recall my initial reaction to the section conjecture: Thanks Thiery for correcting my misconception. Leo Alonso 5, 2 22 Szpiro, meanwhile, had a very lively interest in the Mordell conjecture, as you can see from his writings and seminars in the late 70’s and early eet.