There’s one part of the “Scholze’s perfectoid spaces are the right idea” story that isn’t really mentioned here that I don’t quite understand, but I think is important for understanding it’s story. As it happens, Scholze was not the only one to discover the concept of perfectoid spaces and the tilting correspondence—Kedlaya and Liu also develop essentially the same theory in “Relative p-adic hodge theory: Foundations”, but with a different proof of the main result (the tilting correspondence).
The aftermath looks a lot like the result of a historian’s “social power struggle”. By all accounts the two works were independent. According to the introduction of Kedlaya-Liu, these authors had begun to disseminate their work before Scholze’s work went public in 2010. At that point, Scholze’s work “went viral”, causing Scholze to become a widely known mathematician. The other two authors reformulated their paper in terms of Scholze’s language and it was put on the arXiv in 2013, well after Scholze’s formulation was widely popular. Nowadays, most people give all of the credit for the discovery to Scholze, not even mentioning Kedlaya and Liu, much like the above article does. And off the record one can sometimes hear grumbles from researchers who are aware of Kedlaya-Liu’s work. Scholze is cooler, younger, and whiter that either of the other two authors.
As far as I can tell, the potential advantages that Scholze’s formalism has are
1) Slightly simpler foundations
2) The name “perfectoid” to illustrate a certain concept, which did not have a name in Kedlaya-Liu
3) Some simpler notation
4) The application to the Weight-Monodromy conjecture
So my question is the following: what exactly makes Scholze’s formalism the “right one” as compared to Kedlaya-Liu? Is it something from (1)-(4)? Is it something I’ve missed? Is it the fact that Scholze disseminated his research much quicker than Kedlaya-Liu? Or is it a more “social” concern, the tyranny of the “young white hotshot mathematician” or something like that? A combination of these factors?
There’s one part of the “Scholze’s perfectoid spaces are the right idea” story that isn’t really mentioned here that I don’t quite understand, but I think is important for understanding it’s story. As it happens, Scholze was not the only one to discover the concept of perfectoid spaces and the tilting correspondence—Kedlaya and Liu also develop essentially the same theory in “Relative p-adic hodge theory: Foundations”, but with a different proof of the main result (the tilting correspondence).
The aftermath looks a lot like the result of a historian’s “social power struggle”. By all accounts the two works were independent. According to the introduction of Kedlaya-Liu, these authors had begun to disseminate their work before Scholze’s work went public in 2010. At that point, Scholze’s work “went viral”, causing Scholze to become a widely known mathematician. The other two authors reformulated their paper in terms of Scholze’s language and it was put on the arXiv in 2013, well after Scholze’s formulation was widely popular. Nowadays, most people give all of the credit for the discovery to Scholze, not even mentioning Kedlaya and Liu, much like the above article does. And off the record one can sometimes hear grumbles from researchers who are aware of Kedlaya-Liu’s work. Scholze is cooler, younger, and whiter that either of the other two authors.
As far as I can tell, the potential advantages that Scholze’s formalism has are
1) Slightly simpler foundations
2) The name “perfectoid” to illustrate a certain concept, which did not have a name in Kedlaya-Liu
3) Some simpler notation
4) The application to the Weight-Monodromy conjecture
So my question is the following: what exactly makes Scholze’s formalism the “right one” as compared to Kedlaya-Liu? Is it something from (1)-(4)? Is it something I’ve missed? Is it the fact that Scholze disseminated his research much quicker than Kedlaya-Liu? Or is it a more “social” concern, the tyranny of the “young white hotshot mathematician” or something like that? A combination of these factors?