The central equation, "T = {(S, X_S)}", suggests it's a set of pairs consisting of an object "S" and a corresponding "X_S". This kind of notation is typical in sheaf theory or moduli spaces. Key terms visible: "pf of old space / F_t" indicates a proof related to an old spatial structure, possibly algebraic or geometric, with "F_t" representing a function or object family indexed by "t". "thickening" in algebraic geometry refers to the extension of a scheme or structure. "ff curve of S" where "ff" might mean "faithfully flat", important in fiber products and base change theories, with "Curve of S" implying a curve associated with "S".
A couple of clarifications regarding the key terms you pointed out: 1) It's not "pf of old space/F_1", its "perfectoid space/ mathbb{F}_p". where mathbb{F}_p is a field on p-adic numbers. 2) The thickening is specifically defined as a "nil-thickening". I'm not 100% sure what that is and have yet to find a definition. Probably best to consult one of Prof. Scholze's papers for the definition. (EDIT: After a little searching, I'm about 92% sure "nil thickening" and "nilpotent thickening" are the same thing) In general, I'd check out Prof Scholze's work on perfectoid spaces. It should help to clear up any confusion coming from the short-hand notation he uses on the board.
The central equation, "T = {(S, X_S)}", suggests it's a set of pairs consisting of an object "S" and a corresponding "X_S". This kind of notation is typical in sheaf theory or moduli spaces.
Key terms visible:
"pf of old space / F_t" indicates a proof related to an old spatial structure, possibly algebraic or geometric, with "F_t" representing a function or object family indexed by "t".
"thickening" in algebraic geometry refers to the extension of a scheme or structure.
"ff curve of S" where "ff" might mean "faithfully flat", important in fiber products and base change theories, with "Curve of S" implying a curve associated with "S".
A couple of clarifications regarding the key terms you pointed out:
1) It's not "pf of old space/F_1", its "perfectoid space/ mathbb{F}_p". where mathbb{F}_p is a field on p-adic numbers.
2) The thickening is specifically defined as a "nil-thickening". I'm not 100% sure what that is and have yet to find a definition. Probably best to consult one of Prof. Scholze's papers for the definition. (EDIT: After a little searching, I'm about 92% sure "nil thickening" and "nilpotent thickening" are the same thing)
In general, I'd check out Prof Scholze's work on perfectoid spaces. It should help to clear up any confusion coming from the short-hand notation he uses on the board.
awesome, don't fully grasp it, but gives a huge brain buzz