Illinois Journal of Mathematics

Homological conjectures, old and new

Melvin Hochster

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Abstract

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.

Article information

Source
Illinois J. Math., Volume 51, Number 1 (2007), 151-169.

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735330

Digital Object Identifier
doi:10.1215/ijm/1258735330

Mathematical Reviews number (MathSciNet)
MR2346192

Zentralblatt MATH identifier
1127.13010

Subjects
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]

Citation

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


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