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- W3199497639 abstract "Tight closure test ideals have been central to the classification of singularities in rings of characteristic <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p greater-than 0> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>p>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and via reduction to characteristic <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p greater-than 0> <mml:semantics> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>p>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, in equal characteristic 0 as well. Their properties and applications have been described by Schwede and Tucker [<italic>Progress in commutative algebra 2</italic>, 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." @default.
- W3199497639 created "2021-09-27" @default.
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- W3199497639 date "2021-09-14" @default.
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- W3199497639 title "Characteristic-free test ideals" @default.
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- W3199497639 doi "https://doi.org/10.1090/btran/55" @default.
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