# Where does one learn the algebraic geometry needed for topos theory?

I am a masters student familiar with category theory. I have started learning topos theory from MacLane-Moerdijk's book "Sheaves in Geometry and Logic: A First Introduction to topos Theory". I get the feeling that topos theory has a "logic" part and an "algebraic geometry" part. I am not interested in logic and I am not familiar with algebraic geometry at all. I am though interested in abstract algebra and thus if it has to be one of the two directions, it must be algebraic geometry.

I would like to ask if there is any treatment in the literature of the algebraic geometry needed for a category theorist to become comfortable with notions like the étale and Zariski sites etc. I have heard many people mentioning Grothendieck's EGA when discussing topos theory. But I find this very difficult to read. What do I need to know in order to attempt studying it? Of course in the mentioned book (MacLane-Moerdijk) one can find the elements needed to get an idea of some constructions, but I think that it does not give the big picture. Or do I have to learn algebraic geometry from scratch?

• Why do you want to learn topos theory? Algebraic geometry is the branch of mathematics which has made the most use of topos theory, but you do not need to know any algebraic geometry to learn topos theory. Feb 22, 2014 at 16:54
• Just reviewing here (that happens to everybody's first question) can you cite the titles of the books you refer to in full, (at least title and year ) Feb 22, 2014 at 17:03
• Why do I want to learn topos theory? Why should I not want to learn it? I mean, there is no need to, but it seems like an area that puts a lot of category theory's ideas in practice. I agree that you don't need algebraic geometry to learn topos theory, but saying this is like saying that one does not need algebra and topology for learning category theory. Something which is true, but not effective in my opinion... Feb 22, 2014 at 17:32
• I don't think that EGA covers topos theory. But SGA does. Feb 22, 2014 at 18:57