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I'm an applied mathematician, computer scientist, physicist. I have some basic knowledge of algebraic geometry. Books like this: https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/ crop up every now and again with Grothendieck's inevitably influences on these subjects.

When I come across them/need to top up, I think "I should just learn from the master himself". Unfortunately, almost everything he's written is 10,000 pages long or in French or... :) Whilst on the other hand a textbook on algebraic geometry/category theory, may be in the same field, but have ultimately none of 'his' ideas as such (even if they are built on his foundations).

Have there ever been introduction books (grad level) that basically are able to walk us through specifically his maths/ideas? It is also hard to see with such a large landscape where one should begin with Grothendieck. What is the best way to learn directly from Grothendieck's ideas?

Socorro
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  • There are fairly elementary introductions to Grothendiecks "anabelian geometry", because of the "popular" interest in the $abc$-conjecture and Mochizuki's work involving anabelian geometry. You can search, e.g. for introductory slides by Florian Pop. This site also has some posts, e.g., this one, and others. – Dietrich Burde Sep 17 '22 at 09:24

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