Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 51, Number 1 (2007), 151-169.
Homological conjectures, old and new
We discuss a number of the local homological conjectures, many of which are now theorems in equal characteristic and conjectures in mixed characteristic. One focus is the syzygy theorem of Evans and Griffith, and its connection with the direct summand conjecture, the existence of big Cohen-Macaulay modules and algebras, and tight closure theory.
Illinois J. Math., Volume 51, Number 1 (2007), 151-169.
First available in Project Euclid: 20 November 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D22: Homological conjectures (intersection theorems)
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 13D45: Local cohomology [See also 14B15]
Hochster, Melvin. Homological conjectures, old and new. Illinois J. Math. 51 (2007), no. 1, 151--169. doi:10.1215/ijm/1258735330. https://projecteuclid.org/euclid.ijm/1258735330