Motivic Serre invariants, ramification, and the analytic Milnor fiber

DOI10.1007/s00222-006-0029-7zbMath1136.14010arXivmath/0703217OpenAlexW3105411107MaRDI QIDQ2457767

Julien Sebag, Johannes Nicaise

Publication date: 23 October 2007

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703217

zbMATH Keywords

monodromymotivic integrationMilnor fiberIgusa's local zeta function

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Étale and other Grothendieck topologies and (co)homologies (14F20) Local ground fields in algebraic geometry (14G20)

Related Items (39)

Logarithmic geometry and the Milnor fibration ⋮ Trace formulas for motivic volumes ⋮ Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero ⋮ A short survey on the integral identity conjecture and theories of motivic integration ⋮ Motivic Milnor fibre of cyclic \(L_\infty\)-algebras ⋮ On Grothendieck rings and algebraically constructible functions ⋮ Nearby motives and motivic nearby cycles ⋮ Computing motivic zeta functions on log smooth models ⋮ Motivic Serre invariants of curves ⋮ Motivic Serre invariants modulo the square of 𝕃-1 ⋮ The Thom-Sebastiani theorem for the Euler characteristic of cyclic \(L_\infty\)-algebras ⋮ Geometric criteria for tame ramification ⋮ Nearby motivic sheaves of weighted equivariant functions ⋮ Motivic zeta functions of degenerating Calabi-Yau varieties ⋮ On motivic vanishing cycles of critical loci ⋮ Motivic Milnor fibers of a rational function ⋮ Virtual rigid motives of semi-algebraic sets ⋮ Motivic invariants of algebraic tori ⋮ The global monodromy property for \(K3\) surfaces allowing a triple-point-free model ⋮ The motivic Thom-Sebastiani theorem for regular and formal functions ⋮ Motivic zeta functions of Abelian varieties, and the monodromy conjecture ⋮ The Serre invariant and the analytic Milnor fiber. ⋮ Proofs of the integral identity conjecture over algebraically closed fields ⋮ Tropical refined curve counting via motivic integration ⋮ Real Milnor Fibres and Puiseux Series ⋮ The quotient map on the equivariant Grothendieck ring of varieties ⋮ A trace formula for rigid varieties, and motivic Weil generating series for formal schemes ⋮ Volume and symplectic structure for \(\ell\)-adic local systems ⋮ Convergence of \(p\)-adic pluricanonical measures to Lebesgue measures on skeleta in Berkovich spaces ⋮ A trace formula for varieties over a discretely valued field ⋮ Singular cohomology of the analytic Milnor fiber, and mixed Hodge structure on the nearby cohomology ⋮ Equivariant motivic integration and proof of the integral identity conjecture for regular functions ⋮ Links of sandwiched surface singularities and self-similarity ⋮ Artin motives, weights, and motivic nearby sheaves ⋮ Equivariant motivic integration on formal schemes and the motivic zeta function ⋮ Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry ⋮ Evaluation of motivic functions, non-nullity, and integrability in fibers ⋮ Computing zeta functions on log smooth models ⋮ The moduli space of stable coherent sheaves via non-Archimedean geometry

Cites Work

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• Lefschetz numbers of iterates of the monodromy and truncated arcs
• Toroidal embeddings. I
• Motivic Serre invariants of curves
• Constructible motivic functions and motivic integration
• La fonction zeta d'une monodromie
• Germs of arcs on singular algebraic varieties and motivic integration
• Irreducible components of rigid spaces
• Étale cohomology for non-Archimedean analytic spaces
• Néron models in the setting of formal and rigid geometry
• Motivic integration on smooth rigid varieties and invariants of degenerations
• La conjecture de Weil. I
• The Grothendieck ring of varieties is not a domain.
• Formal and rigid geometry. III: The relative maximum principle
• Crystalline Dieudonné module theory via formal and rigid geometry
• Vanishing cycles for formal schemes. II
• Lectures on formal and rigid geometry
• Motivic Serre invariants and Weil restriction
• The Serre invariant and the analytic Milnor fiber.
• Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas. (Première partie). Rédigé avec la colloboration de J. Dieudonné
• A simplified proof of desingularization and applications
• Néron Models
• The Geometry of Schemes
• Poles of Zeta Functions on Normal Surfaces
• Intégration motivique sur les schémas formels
• Singular Points of Complex Hypersurfaces. (AM-61)

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