Motivic Milnor Fibre of Cyclic L∞-algebras
نویسنده
چکیده
We define motivic Milnor fibre of cyclic L∞-algebras of dimension three using the method of Denef and Loeser of motivic integration. It is proved by Nicaise and Sebag that the topological Euler characteristic of the motivic Milnor fiber is equal to the Euler characteristic of the étale cohomology of the analytic Milnor fiber. We prove that the value of Behrend function on the germ moduli space determined by L is equal to the Euler characteristic of the analytic Milnor fiber. Thus we prove that Behrend function depends only on the formal neighborhood of the moduli space.
منابع مشابه
An Overview of Motivic Cohomology
In this talk we give an overview of some of the motivations behind and applications of motivic cohomology.We first present aK-theoretic timeline converging onmotivic cohomology, then briefly discuss algebraic K-theory and its more concrete cousin Milnor K-theory. We then present a geometric definition of motivic cohomology via Bloch’s higher Chow groups and outline the main features of motivic ...
متن کاملVanishing Cycles in Complex Symplectic Geometry
We study the vanishing cycles on the Milnor fibre for some non-isolated singularities which appear naturally in symplectic geometry. Under assumptions given in the text, we show that the vanishing cycles associated to a distinguish basis freely generate the corresponding homology groups of the Milnor fibre. We derive some consequences of this fact, in particular for the study of adjoint orbits ...
متن کاملMotivic E∞-algebras and the Motivic Dga
In this paper we define an E∞-structure, i.e. a coherently homotopy associative and commutative product on chain complexes defining (integral and mod-l) motivic cohomology as well as mod -l étale cohomology. We also discuss several applications.
متن کاملThe Milnor Conjecture
3 Motivic cohomology and algebraic cobordisms. 21 3.1 A topological lemma. . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Homotopy categories of algebraic varieties . . . . . . . . . . . 25 3.3 Eilenberg-MacLane spectra and motivic cohomology. . . . . . . 30 3.4 Topological realization functor. . . . . . . . . . . . . . . . . . . 33 3.5 Algebraic cobordisms. . . . . . . . . . . . . . . . ...
متن کاملCohomology operations and algebraic geometry
This manuscript is based on a ten hours series of seminars I delivered in August of 2003 at the Nagoya Institute of Technology as part of the workshop on homotopy theory organized by Norihiko Minami and following the Kinosaki conference in honor of Goro Nishida. One of the most striking applications of homotopy theory in “exotic” contexes is Voevodsky’s proof of the Milnor Conjecture. This conj...
متن کامل