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• W4360844186 abstract "In this paper, we study the minimal model theory for threefolds in mixed characteristic. As a generalization of a result of Kawamata, we show that the minimal model program (MMP) holds for strictly semi-stable schemes over an excellent Dedekind scheme <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper V> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=application/x-tex>V</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of relative dimension two without any assumption on the residue characteristics of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper V> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=application/x-tex>V</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We also prove that we can run a <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper K Subscript upper X slash upper V Baseline plus normal upper Delta right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>K</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>X</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>V</mml:mi> </mml:mrow> </mml:msub> <mml:mo>+</mml:mo> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(K_{X/V}+Delta )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-MMP over <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper Z> <mml:semantics> <mml:mi>Z</mml:mi> <mml:annotation encoding=application/x-tex>Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=pi colon upper X right-arrow upper Z> <mml:semantics> <mml:mrow> <mml:mi>π<!-- π --></mml:mi> <mml:mo>:<!-- : --></mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=false>→<!-- → --></mml:mo> <mml:mi>Z</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>pi colon X to Z</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a projective birational morphism of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=double-struck upper Q> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>Q</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>mathbb {Q}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-factorial quasi-projective <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper V> <mml:semantics> <mml:mi>V</mml:mi> <mml:annotation encoding=application/x-tex>V</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-schemes and <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper X comma normal upper Delta right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>,</mml:mo> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(X,Delta )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a three-dimensional dlt pair with <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper E x c left-parenthesis pi right-parenthesis subset-of left floor normal upper Delta right floor> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mi>x</mml:mi> <mml:mi>c</mml:mi> <mml:mo stretchy=false>(</mml:mo> <mml:mi>π<!-- π --></mml:mi> <mml:mo stretchy=false>)</mml:mo> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mo fence=false stretchy=false>⌊<!-- ⌊ --></mml:mo> <mml:mi mathvariant=normal>Δ<!-- Δ --></mml:mi> <mml:mo fence=false stretchy=false>⌋<!-- ⌋ --></mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Exc(pi ) subset lfloor Delta rfloor</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
• W4360844186 created "2023-03-25" @default.
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• W4360844186 date "2023-03-24" @default.
• W4360844186 modified "2023-10-01" @default.
• W4360844186 title "Minimal model program for semi-stable threefolds in mixed characteristic" @default.
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• W4360844186 doi "https://doi.org/10.1090/jag/813" @default.
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