2007/01/01 by Melvin Hochster · 1 citation
Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Closure (psychology) #Commutative Algebra and Its Applications #Conjecture #Connection (principal bundle) #Geometry #Hilbert's syzygy theorem #Law #Mathematics #Pure mathematics
paper · pdf · doi:10.1215/ijm/1258735330
openalex publication_date 2007/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
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.