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Charles Matthews
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Who will write the algebraic geometry texts that are needed?

Readers of MO are probably aware of the pedagogic need that would provoke such a query. It's around 60 years since Serre's FAC, and I imagine some people would say "you still have to read the original papers". There are well-known issues with the EGA/SGA material, and they can be met only by extensive rewriting. While there are some highly competent (IMO) authors dealing with aspects, an integrated treatment seems a long way off.

So, who has an overview? And who might be able to pull together a treatment of the whole area? We've come a long way since Zariski's Algebraic Surfaces, in particular, which de facto drew a line under the Italian school.

Charles Matthews
  • 12.6k
  • 35
  • 64