scholarly journals Closure operations that induce big Cohen–Macaulay modules and classification of singularities

2016 ◽  
Vol 467 ◽  
pp. 237-267 ◽  
Author(s):  
Rebecca R.G.
Keyword(s):  
Closure Operations ◽  
Classification Of Singularities

scholarly journals Characteristic-free test ideals

2021 ◽  
Vol 8 (24) ◽  
pp. 754-787
Author(s):  
Felipe Pérez ◽  
Rebecca R. G.
Keyword(s):  
Commutative Algebra ◽  
Tight Closure ◽  
Content Type ◽  
Mixed Characteristic ◽  
Closure Operations ◽  
Characteristic Case ◽  
Test Ideal ◽  
Classification Of Singularities ◽  
Free Classification

Tight closure test ideals have been central to the classification of singularities in rings of characteristic p > 0 p>0 , and via reduction to characteristic p > 0 p>0 , in equal characteristic 0 as well. Their properties and applications have been described by Schwede and Tucker [Progress in commutative algebra 2, Walter de Gruyter, Berlin, 2012]. In this paper, we extend the notion of a test ideal to arbitrary closure operations, particularly those coming from big Cohen-Macaulay modules and algebras, and prove that it shares key properties of tight closure test ideals. Our main results show how these test ideals can be used to give a characteristic-free classification of singularities, including a few specific results on the mixed characteristic case. We also compute examples of these test ideals.

The classification of singularities

1975 ◽  
Vol 6 (1) ◽  
pp. 35-40 ◽  
Author(s):  
C. J. S. Clarke
Keyword(s):  
Classification Of Singularities

Complete transversals and the classification of singularities

Nonlinearity ◽  
1997 ◽  
Vol 10 (1) ◽  
pp. 253-275 ◽  
Author(s):  
J W Bruce ◽  
N P Kirk ◽  
A A du Plessis
Keyword(s):  
Classification Of Singularities
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