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• W1482216487 abstract "Given a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=application/x-tex>B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module <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> and any presentation <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B equals upper A slash upper J> <mml:semantics> <mml:mrow> <mml:mi>B</mml:mi> <mml:mo>=</mml:mo> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>J</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>B=A/J</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, the obstruction theory of <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> as a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=application/x-tex>B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module is determined by the usual obstruction class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal o Subscript upper A Superscript> <mml:semantics> <mml:msubsup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>o</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mspace width=negativethinmathspace /> <mml:mstyle displaystyle=false scriptlevel=2> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>A</mml:mi> </mml:mrow> </mml:mstyle> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mstyle displaystyle=false scriptlevel=2> <mml:mrow class=MJX-TeXAtom-ORD> </mml:mrow> </mml:mstyle> </mml:mrow> </mml:msubsup> <mml:annotation encoding=application/x-tex>mathrm {o}_{! scriptscriptstyle {A}}^{scriptscriptstyle {}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for deforming <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> as an <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module <italic>and</italic> a new obstruction class <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal o Subscript upper J Superscript> <mml:semantics> <mml:msubsup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=normal>o</mml:mi> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mspace width=negativethinmathspace /> <mml:mstyle displaystyle=false scriptlevel=2> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>J</mml:mi> </mml:mrow> </mml:mstyle> </mml:mrow> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mstyle displaystyle=false scriptlevel=2> <mml:mrow class=MJX-TeXAtom-ORD> </mml:mrow> </mml:mstyle> </mml:mrow> </mml:msubsup> <mml:annotation encoding=application/x-tex>mathrm {o}_{! scriptscriptstyle {J}}^{scriptscriptstyle {}}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . These two classes give the tool for constructing two obstruction maps which depend on each other and which characterise the hull of the deformation functor. We obtain relations between the obstruction classes by studying a change of rings spectral sequence and by representing certain classes as elements in the Yoneda complex. Calculation of the deformation functor of <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> as a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper B> <mml:semantics> <mml:mi>B</mml:mi> <mml:annotation encoding=application/x-tex>B</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-module, including the (generalised) Massey products, is thus possible within any <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-free <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=2> <mml:semantics> <mml:mn>2</mml:mn> <mml:annotation encoding=application/x-tex>2</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-presentation of <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>." @default.
• W1482216487 created "2016-06-24" @default.
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• W1482216487 date "2004-01-29" @default.
• W1482216487 modified "2023-09-23" @default.
• W1482216487 title "Change of rings in deformation theory of modules" @default.
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