On deformations of pasting diagrams.
On exact modules over a commutative exact ring
On multi-Rees algebras. With an Appenddix by Ngô Viêt Trung.
On Products in a Family of Cohomology Theories Associated to the Invariant Prime Ideals of ... (BP).
On the Betti numbers of perfect ideals
On the free character of the first Koszul homology module.
Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1(E) is a free A/I-module.- (André [2]): Assume that A is a complete...
On the graded Betti numbers for large finite subsets of curves
We prove a recent conjecture of S. Lvovski concerning the periodicity behaviour of top Betti numbers of general finite subsets with large cardinality of an irreducible curve C ⊂ ℙⁿ.
On the homology of some special complexes. (Sobre la homología de algunos complejos especiales.)
On the non-vanishing of cotangent cohomology.
On the Steenrod operations in cyclic cohomology.
On the upper semicontinuity intersection defect.
Opérations sur l'homologie cyclique des algèbres commutatives.
Orientations and multiplicative structures of resolutions.
p-adic semi-algebraic sets and cell decomposition.
Pascal type properties of Betti numbers.
Poincaré duality and commutative differential graded algebras
We prove that every commutative differential graded algebra whose cohomology is a simply-connected Poincaré duality algebra is quasi-isomorphic to one whose underlying algebra is simply-connected and satisfies Poincaré duality in the same dimension. This has applications in rational homotopy, giving Poincaré duality at the cochain level, which is of interest in particular in the study of configuration spaces and in string topology.
Pojective exterior Koszul homology and decomposititon of the Tor fonctor.
Produit tensoriel et complexe cotangent.
Rational BV-algebra in string topology
Let be a 1-connected closed manifold of dimension and be the space of free loops on . M.Chas and D.Sullivan defined a structure of BV-algebra on the singular homology of , . When the ring of coefficients is a field of characteristic zero, we prove that there exists a BV-algebra structure on the Hochschild cohomology which extends the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between and the shifted homology . We also prove that the...
Reg ouvert et complexe cotangent.