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Affine braid group actions on derived categories of Springer resolutions

Roman Bezrukavnikov, Simon Riche (2012)

Annales scientifiques de l'École Normale Supérieure

In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...

Albanese varieties with modulus and Hodge theory

Kazuya Kato, Henrik Russell (2012)

Annales de l’institut Fourier

Let X be a proper smooth variety over a field k of characteristic 0 and Y an effective divisor on X with multiplicity. We introduce a generalized Albanese variety Alb ( X , Y ) of X of modulus Y , as higher dimensional analogue of the generalized Jacobian with modulus of Rosenlicht-Serre. Our construction is algebraic. For k = ℂ we give a Hodge theoretic description.

Algebraic and symplectic Gromov-Witten invariants coincide

Bernd Siebert (1999)

Annales de l'institut Fourier

For a complex projective manifold Gromov-Witten invariants can be constructed either algebraically or symplectically. Using the versions of Gromov-Witten theory by Behrend and Fantechi on the algebraic side and by the author on the symplectic side, we prove that both points of view are equivalent

Algebraic cobordism of bundles on varieties

Y.-P. Lee, Rahul Pandharipande (2012)

Journal of the European Mathematical Society

The double point relation defines a natural theory of algebraic cobordism for bundles on varieties. We construct a simple basis (over ℚ ) of the corresponding cobordism groups over Spec( ℂ ) for all dimensions of varieties and ranks of bundles. The basis consists of split bundles over products of projective spaces. Moreover, we prove the full theory for bundles on varieties is an extension of scalars of standard algebraic cobordism.

Algebraic equivalence of real algebraic cycles

Miguel Abánades, Wojciech Kucharz (1999)

Annales de l'institut Fourier

Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

Algebraic homotopy classes of rational functions

Christophe Cazanave (2012)

Annales scientifiques de l'École Normale Supérieure

Let  k be a field. We compute the set 𝐏 1 , 𝐏 1 N ofnaivehomotopy classes of pointed k -scheme endomorphisms of the projective line 𝐏 1 . Our result compares well with Morel’s computation in [11] of thegroup 𝐏 1 , 𝐏 1 𝐀 1 of  𝐀 1 -homotopy classes of pointed endomorphisms of  𝐏 1 : the set 𝐏 1 , 𝐏 1 N admits an a priori monoid structure such that the canonical map 𝐏 1 , 𝐏 1 N → 𝐏 1 , 𝐏 1 𝐀 1 is a group completion.

Algebraic tori as Nisnevich sheaves with transfers

Bruno Kahn (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

We relate R -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.

Currently displaying 101 – 120 of 170