cohomologie non ramifiee et conjecture de hodge entiere en nous appuyant sur la conjecture de bloch kato en k theorie de milnor nous etablissons un lien general entre le defaut de la conjecture de hodge entiere pour la cohomologie de degre 4 et le troisieme groupe de cohomologie non ramifiee a coefficients q z ceci permet de montrer que sur un solide en anglais threefold uniregle le troisieme groupe de cohomologie non ramifiee a coefficients q z s annule ce que la k theorie algebrique ne permet d obtenir que dans certains cas ceci permet a l inverse de deduire d exemples ayant leur source en k theorie que la conjecture de hodge entiere pour la cohomologie de degre 4 peut etre en defaut pour les varietes rationnellement connexes pour certaines familles a un parametre de surfaces on etablit un lien entre la conjecture de hodge entiere et l indice de la fibre generique

semilinear integro differential equations i odd solutions with respect to the simons cone abstract this is the first of two papers concerning saddle shaped solutions to the semilinear equation l k u f u in r 2 m where l k is a linear elliptic integro differential operator and f is of allen cahn type saddle shaped solutions are doubly radial odd with respect to the simons cone x x r m r m x x and vanish only on this set by the odd symmetry l k coincides with a new operator l k o which acts on functions defined only on one side of the simons cone x x and that vanish on it this operator l k o which corresponds to reflect a function oddly and then apply l k has a kernel on x x which is different from k in this first paper we characterize the kernels k for which the new kernel is positive and therefore one can develop a theory on the saddle shaped solution the necessary and sufficient condition for this turns out to be that k is radially symmetric and k is a strictly convex function assuming this we prove an energy estimate for doubly radial odd minimizers and the existence of saddle shaped solution in a subsequent article part ii further qualitative properties of saddle shaped solutions will be established such as their asymptotic behavior a maximum principle for the linearized operator and their uniqueness

modularity of relatively rational vertex algebras and fusion rules of principal affine w algebras we study modularity of the characters of a vertex super algebra equipped with a family of conformal structures along the way we introduce the notions of rationality and cofiniteness relative to such a family we apply the results to determine modular transformations of trace functions on admissible modules over affine kac moody algebras and via brst reduction trace functions on minimal series representations of principal affine w algebras

modularity of n point functions and theta functions for vertex operator superalgebras abstract the modularity of the n point trace functions and theta functions associated with vertex operator superalgebras are established

modularity in orbifold theory for vertex operator superalgebras this paper is about the orbifold theory for vertex operator superalgebras given a vertex operator superalgebra v and a finite automorphism group g of v we show that the trace functions associated to the twisted sectors are holomorphic in the upper half plane for any commuting pairs in g under the c2 cofinite condition we also establish that these functions afford a representation of the full modular group if v is c2 cofinite and g rational for any g g

unramified cohomology of quadrics i given a quadric x over a field f of characteristic 2 we compute the kernel and cokernel of the natural map in degree 4 from the mod 2 galois cohomology of f to the unramified mod 2 cohomology of f x when dim x 10 and in several smaller dimensional cases applications of these results to real quadrics and to the unramified witt ring are given

2 cycles sur les hypersurfaces cubiques de dimension 5 we study 2 cycles of a smooth cubic hypersurface of dimension 5 we show that the griffiths group of 2 cycles is trivial and the abel jacobi map induces an isomorphism between the chow group of algebraically trivial 2 cycles and the intermediate jacobian

on motivic cohomology with z l coefficients in this paper we prove the conjecture of bloch and kato which relates milnor s k theory of a field with its galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the nisnevich and etale topologies

near sphere lattices with constant nonlocal mean curvature we are concerned with unbounded sets of mathbb r n whose boundary has constant nonlocal or fractional mean curvature which we call cnmc sets this is the equation associated to critical points of the fractional perimeter functional under a volume constraint we construct cnmc sets which are the countable union of a certain bounded domain and all its translations through a periodic integer lattice of dimension m le n our cnmc sets form a c 2 branch emanating from the unit ball alone and where the parameter in the branch is essentially the distance to the closest lattice point thus the new translated near balls or near spheres appear from infinity we find their exact asymptotic shape as the parameter tends to infinity

varietes unirationnelles non rationnelles au dela de l exemple d artin et mumford keywords non rational but unirational variety grothendieck invariants rationality brauer invariants reference cma article 1989 001doi 10 1007 bf01850658 record created on 2008 12 16 modified on 2016 08 08

stably irrational hypersurfaces of small slopes we show that over any uncountable field of characteristic different from two a very general hypersurface of dimension n 2 and degree at least log 2 n 2 is not stably rational this significantly improves earlier results of kollar and totaro as a byproduct of our proof we obtain new counterexamples to the integral hodge conjecture answering a question of voisin and colliot thelene voisin

calculus of twisted vertex operators starting from an arbitrary isometry of an arbitrary even lattice twisted and shifted vertex operators are introduced under commutators these operators provide realizations of twisted affine lie algebras this construction generalizing a number of known ones is based on a self contained calculus

one point theta functions for vertex operator algebras abstract one point theta functions for modules of vertex operator algebras voas are defined and studied these functions are a generalization of the character theta functions studied by miyamoto and are deviations of the classical one point functions for modules of a voa transformation laws with respect to the group sl 2 z are established

nonlocal s minimal surfaces and lawson cones nserc of canada fondecyt 1130360 1150066 fondo basal cmm millenium nucleus capde nc130017

some spectral sequences for filtered complexes and applications abstract we construct a hierarchy of spectral sequences for a filtered complex under a left exact functor as applications we prove 1 the existence of a leray spectral sequence for de rham cohomology 2 the equivalence of this sequence with the usual leray spectral spectral sequence under the comparison isomorphism and 3 the isomorphism of the bloch ogus spectral sequence with the leray spectral sequence for the morphism from the fine site to the zariski site

characters of topological n 2 vertex algebras are jacobi forms on the moduli space of elliptic supercurves abstract we show that trace functions on modules of topological n 2 super vertex algebras give rise to conformal blocks on elliptic supercurves we show that they satisfy a system of linear partial differential equations with respect to the modular parameters of the supercurves under some finiteness condition on the vertex algebra these differential equations can be interpreted as a connection on the vector bundle of conformal blocks we show that this connection is equivariant with respect to a natural action of the jacobi modular group on the modular parameters and the trace functions in the appendix we prove the convergence of the trace functions