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- W2031619782 abstract "Let <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=application/x-tex>M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a finitely generated module over a local complete intersection <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper R> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding=application/x-tex>R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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>. The property that <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper M> <mml:semantics> <mml:mi>M</mml:mi> <mml:annotation encoding=application/x-tex>M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has finite projective dimension can be characterized by the vanishing of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=e x t Subscript upper R Superscript i Baseline left-parenthesis Superscript f Super Superscript n Superscript Baseline upper R comma upper M right-parenthesis> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>ext</mml:mi> <mml:mi>R</mml:mi> <mml:mi>i</mml:mi> </mml:msubsup> <mml:mo><!-- --></mml:mo> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:msup> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:msup> <mml:mspace width=negativethinmathspace /> <mml:mspace width=negativethinmathspace /> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>operatorname {ext}_R^i({}^{f^n}!! R,M)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for some <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=i greater-than 0> <mml:semantics> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>i>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and for some <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n greater-than 0> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding=application/x-tex>n>0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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- W2031619782 creator A5044294711 @default.
- W2031619782 date "2005-10-13" @default.
- W2031619782 modified "2023-09-27" @default.
- W2031619782 title "Characterization of modules of finite projective dimension over complete intersections" @default.
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