On motivic zeta functions and the motivic nearby fiber

DOI10.1007/s00209-004-0689-1zbMath1085.14020arXivmath/0307033OpenAlexW2054214024MaRDI QIDQ1769032

Franziska Bittner

Publication date: 16 March 2005

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307033

zbMATH Keywords

motivic zeta functionmotivic nearby fiber

Mathematics Subject Classification ID

Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Deformations of complex singularities; vanishing cycles (32S30) Motivic cohomology; motivic homotopy theory (14F42)

Related Items (28)

Singularités à l’infini et intégration motivique ⋮ Motivic integration and Milnor fiber ⋮ Tropical geometry, the motivic nearby fiber, and limit mixed Hodge numbers of hypersurfaces ⋮ Mixed Hodge Structures Applied to Singularities ⋮ Motivic Milnor Fibre for Nondegenerate Function Germs on Toric Singularities ⋮ A short survey on the integral identity conjecture and theories of motivic integration ⋮ On Grothendieck rings and algebraically constructible functions ⋮ Nearby motives and motivic nearby cycles ⋮ Motivic Milnor fiber at infinity and composition with a non-degenerate polynomial ⋮ Tropical homology ⋮ EULER CHARACTERISTIC AND SIGNATURE OF REAL SEMI-STABLE DEGENERATIONS ⋮ Lefschetz numbers of Verdier monodromy and the motivic monodromy conjecture for toric varieties ⋮ Verdier specialization via weak factorization ⋮ Motivic degree zero Donaldson-Thomas invariants ⋮ On the motive of the Quot scheme of finite quotients of a locally free sheaf ⋮ Characteristic classes of complex hypersurfaces ⋮ Motivic Milnor fibers of a rational function ⋮ Virtual rigid motives of semi-algebraic sets ⋮ Newton transformations and motivic invariants at infinity of plane curves ⋮ Formulas for monodromy ⋮ Microlocal geometry and valued fields ⋮ Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink ⋮ A tropical motivic Fubini theorem with applications to Donaldson-Thomas Theory ⋮ The quotient map on the equivariant Grothendieck ring of varieties ⋮ The local motivic DT/PT correspondence ⋮ Equivariant motivic integration on formal schemes and the motivic zeta function ⋮ Tropical geometry and the motivic nearby fiber ⋮ Integration over spaces of nonparametrized arcs and motivic versions of the monodromy zeta function

Cites Work

• Unnamed Item
• Unnamed Item
• Lefschetz numbers of iterates of the monodromy and truncated arcs
• Toroidal embeddings. I
• Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
• Introduction to Toric Varieties. (AM-131)
• The universal Euler characteristic for varieties of characteristic zero

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