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• W3203964178 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> denote a finitely generated module over a Noetherian ring <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>. For an ideal <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper I subset-of upper R> <mml:semantics> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mi>R</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>I subset R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> there is a study of the endomorphisms of the local cohomology module <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper H Subscript upper I Superscript g Baseline left-parenthesis upper M right-parenthesis comma g equals g r a d e left-parenthesis upper I comma upper M right-parenthesis comma> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mi>I</mml:mi> <mml:mi>g</mml:mi> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> <mml:mi>r</mml:mi> <mml:mi>a</mml:mi> <mml:mi>d</mml:mi> <mml:mi>e</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>I</mml:mi> <mml:mo>,</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>,</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>H^g_I(M), g = grade(I,M),</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and related results. Another subject is the study of left derived functors of the <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper I> <mml:semantics> <mml:mi>I</mml:mi> <mml:annotation encoding=application/x-tex>I</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic completion <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Lamda Subscript i Superscript upper I Baseline left-parenthesis upper H Subscript upper I Superscript g Baseline left-parenthesis upper M right-parenthesis right-parenthesis> <mml:semantics> <mml:mrow> <mml:msubsup> <mml:mi mathvariant=normal>Λ<!-- Λ --></mml:mi> <mml:mi>i</mml:mi> <mml:mi>I</mml:mi> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:msubsup> <mml:mi>H</mml:mi> <mml:mi>I</mml:mi> <mml:mi>g</mml:mi> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>M</mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Lambda ^I_i(H^g_I(M))</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, motivated by a characterization of Gorenstein rings given in <bold>[25]</bold>. This provides another Cohen-Macaulay criterion. The results are illustrated by several examples. There is also an extension to the case of homomorphisms of two different local cohomology modules." @default.
• W3203964178 created "2021-10-11" @default.
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• W3203964178 date "2021-01-01" @default.
• W3203964178 modified "2023-09-27" @default.
• W3203964178 title "Notes on endomorphisms, local cohomology and completion" @default.
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