0000000001290563

AUTHOR

Paul Arne ØStvær

showing 4 related works from this author

Voisinages tubulaires épointés et homotopie stable à l'infini

2022

We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…

links of singularities[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Motivic homotopy theorypunctured tubular neighborhoods[MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT]stable homotopy at infinityMathematics::Algebraic TopologyMathematics - Algebraic Geometrylinks of singularities.Mathematics::Algebraic Geometryquadratic invariantsMathematics::K-Theory and HomologyFOS: MathematicsAlgebraic Topology (math.AT)14F42 19E15 55P42 14F45 55P57Mathematics - Algebraic TopologyAlgebraic Geometry (math.AG)qua- dratic invariants
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𝔸1-contractibility of affine modifications

2019

We introduce Koras–Russell fiber bundles over algebraically closed fields of characteristic zero. After a single suspension, this exhibits an infinite family of smooth affine [Formula: see text]-contractible [Formula: see text]-folds. Moreover, we give examples of stably [Formula: see text]-contractible smooth affine [Formula: see text]-folds containing a Brieskorn–Pham surface, and a family of smooth affine [Formula: see text]-folds with a higher-dimensional [Formula: see text]-contractible total space.

Pure mathematicsComputer Science::Information RetrievalGeneral Mathematics010102 general mathematicsAstrophysics::Instrumentation and Methods for AstrophysicsZero (complex analysis)Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)01 natural sciencesSuspension (topology)Motivic cohomology0103 physical sciencesComputer Science::General LiteratureFiber bundle010307 mathematical physicsAffine transformation0101 mathematicsAlgebraically closed fieldMathematicsInternational Journal of Mathematics
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Stable motivic homotopy theory at infinity

2021

In this paper, we initiate a study of motivic homotopy theory at infinity. We use the six functor formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under $\ell$-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers the singular complex at in…

[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][MATH.MATH-AT] Mathematics [math]/Algebraic Topology [math.AT]Mathematics::Algebraic TopologyMathematics - Algebraic GeometryMathematics::Algebraic GeometryMathematics::K-Theory and Homology[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]Mathematics::Category TheoryFOS: MathematicsAlgebraic Topology (math.AT)[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Mathematics - Algebraic TopologyPrimary: 14F42 19E15 55P42 Secondary: 14F45 55P57Algebraic Geometry (math.AG)
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Milnor-Witt Motives

2020

We develop the theory of Milnor-Witt motives and motivic cohomology. Compared to Voevodsky's theory of motives and his motivic cohomology, the first difference appears in our definition of Milnor-Witt finite correspondences, where our cycles come equipped with quadratic forms. This yields a weaker notion of transfers and a derived category of motives that is closer to the stable homotopy theory of schemes. We prove a cancellation theorem when tensoring with the Tate object, we compare the diagonal part of our Milnor-Witt motivic cohomology to Minor-Witt K-theory and we provide spectra representing various versions of motivic cohomology in the $\mathbb{A}^1$-derived category or the stable ho…

Mathematics - Algebraic GeometryMathematics::K-Theory and HomologyMathematics::Category Theory11E70 13D15 14F42 19E15 19G38 (Primary) 11E81 14A99 14C35 19D45 (Secondary)FOS: Mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG][MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)Mathematics::Algebraic Topology
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