I am looking for links between tight closure and deformation theory. As a sample question:
Question 1. Are there geometric interpretations in terms of deformation theory of Frobenius rationality?
Any references or helps are appreciated.
Searchign the Mathscinet, gave the the following articles, but I am looking for more explicit results:
1) Brenner, Holger Forcing algebras, syzygy bundles, and tight closure. Commutative algebra—Noetherian and non-Noetherian perspectives, 77–99, Springer, New York, 2011.
2) Sharif, Tirdad On a result of Faltings via tight closure. Proc. Amer. Math. Soc. 138 (2010), no. 10, 3495–3499.
3) Brenner, Holger Tight closure and vector bundles. Three lectures on commutative algebra, 1–71, Univ. Lecture Ser., 42, Amer. Math. Soc., Providence, RI, 2008.
As requested, I know ask something maybe more explicit.
Question 2. What is the relation between F-rationality in tight closure and deformation theory in the sense of Mazur?