The Homological Conjectures: Resolved!

ac.commutative-algebra ag.algebraic-geometry nt.number-theory
Start Date
2018-03-12 
End Date
2018-03-16 
Institution
MSRI 
City
Berkeley, CA 
Country
USA 
Meeting Type
conference 
Homepage
http://www.msri.org/workshops/842 
Contact Name
 

Description

The homological conjectures in commutative algebra are a network of conjectures that have generated a tremendous amount of activity in the last 50 years. They had largely been resolved for commutative rings that contain a field, but, with the exception of some low dimensional cases, several remained open in mixed characteristic --- until recently, when Yves Andr\'e announced a proof of Hochster's Direct Summand Conjecture. The progress comes from systematically applying Scholze's theory of perfectoid spaces, which had already shown its value by solving formidable problems in number theory and representation theory. One of the goals of the workshop is to cover the ingredients going into the proofs of the Direct Summand Conjecture.

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