Student Arithmetic Geometry Seminar: The Derived Direct Summand Conjecture

Seminar | March 3 | 2-3 p.m. | 736 Evans Hall

 Ritvik Ramkumar, UCB

 Department of Mathematics

Let A be a noetherian regular ring and B a finite extension of A. Conjectured by M. Hochster in 1973, the Direct Summand Conjecture asserts that the inclusion map A into B splits, as a map of A-modules. It was quickly seen that the main difficulty lies in the case where A is of mixed characteristic. Finally, in 2016, Y. Andre proved the conjecture by using P. Scholze's theory of perfectoid spaces. Simultaneously, B. Bhatt proved a derived variant of this conjecture and gave a simplified proof of the original conjecture. In this talk, we will discuss the classical conjecture, motivate the use of perfectoid spaces, and give an outline of Bhatt's proof.