Borel-Moore motivic homology and weight structure on mixed motives

By defining and studying functorial properties of the Borel-Moore motivic homology, we identify the heart of Bondarko-H\'ebert's weight structure on Beilinson motives with Corti-Hanamura's category of Chow motives over a base, therefore answering a question of Bondarko

The rigid syntomic ring spectrum

The aim of this paper is to show that Besser syntomic cohomology is representable by a rational ring spectrum in the motivic homotopical sense. In fact, extending previous constructions, we exhibit a simple representability criterion and we apply it to several cohomologies in order to get our central result. This theorem gives new results for syntomic cohomology such as h-descent and the compatibility of cycle classes with Gysin morphisms. Along the way, we prove that motivic ring spectra induces a complete Bloch-Ogus cohomological formalism and even more. Finally, following a general motivic homotopical philosophy, we exhibit a natural notion of syntomic coefficients.Comment: Final version to appear in the Journal de l'institut des Math\'ematiques de Jussieu. Many typos have been corrected and the exposition has been improved according to the suggestions of the referees: we thank them a lot

Contained rupture of a mycotic infrarenal aortic aneurysm infected with Campylobacter fetus.

Mycotic abdominal aortic aneurysms (MAAAs) are rare entities accounting for 0.65-2% of aortic aneurysms. Campylobacter fetus has a tropism for vascular tissue and is a rare cause of mycotic aneurysm. We present a 73-year-old male patient with contained rupture of a MAAA caused by C. fetus, successfully treated with endovascular aortic repair (EVAR) and antibiotics, which is not previously described for this aetiology. Although open surgery is the gold standard, EVAR is nowadays feasible and potentially represents a durable option, especially in frail patients

Equivariant pretheories and invariants of torsors

In the present paper we introduce and study the notion of an equivariant pretheory: basic examples include equivariant Chow groups, equivariant K-theory and equivariant algebraic cobordism. To extend this set of examples we define an equivariant (co)homology theory with coefficients in a Rost cycle module and provide a version of Merkurjev's (equivariant K-theory) spectral sequence for such a theory. As an application we generalize the theorem of Karpenko-Merkurjev on G-torsors and rational cycles; to every G-torsor E and a G-equivariant pretheory we associate a graded ring which serves as an invariant of E. In the case of Chow groups this ring encodes the information concerning the motivic J-invariant of E and in the case of Grothendieck's K_0 -- indexes of the respective Tits algebras.Comment: 23 pages; this is an essentially extended version of the previous preprint: the construction of an equivariant cycle (co)homology and the spectral sequence (generalizing the long exact localization sequence) are adde

Connexin43 Inhibition Prevents Human Vein Grafts Intimal Hyperplasia.

Venous bypass grafts often fail following arterial implantation due to excessive smooth muscle cells (VSMC) proliferation and consequent intimal hyperplasia (IH). Intercellular communication mediated by Connexins (Cx) regulates differentiation, growth and proliferation in various cell types. Microarray analysis of vein grafts in a model of bilateral rabbit jugular vein graft revealed Cx43 as an early upregulated gene. Additional experiments conducted using an ex-vivo human saphenous veins perfusion system (EVPS) confirmed that Cx43 was rapidly increased in human veins subjected ex-vivo to arterial hemodynamics. Cx43 knock-down by RNA interference, or adenoviral-mediated overexpression, respectively inhibited or stimulated the proliferation of primary human VSMC in vitro. Furthermore, Cx blockade with carbenoxolone or the specific Cx43 inhibitory peptide 43gap26 prevented the burst in myointimal proliferation and IH formation in human saphenous veins. Our data demonstrated that Cx43 controls proliferation and the formation of IH after arterial engraftment

Framed transfers and motivic fundamental classes

We relate the recognition principle for infinite P1-loop spaces to the theory of motivic fundamental classes of Deglise, Jin and Khan. We first compare two kinds of transfers that are naturally defined on cohomology theories represented by motivic spectra: the framed transfers given by the recognition principle, which arise from Voevodsky's computation of the Nisnevish sheaf associated with An/(An-0), and the Gysin transfers defined via Verdier's deformation to the normal cone. We then introduce the category of finite R-correspondences for R a motivic ring spectrum, generalizing Voevodsky's category of finite correspondences and Calmes and Fasel's category of finite Milnor-Witt correspondences. Using the formalism of fundamental classes, we show that the natural functor from the category of framed correspondences to the category of R-module spectra factors through the category of finite R-correspondences

Cohomological Hasse principle and motivic cohomology for arithmetic schemes

In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

Motivic Eilenberg-Maclane spaces

This paper is the second one in a series of papers about operations in motivic cohomology. Here we show that in the context of smooth schemes over a field of characteristic zero all the bi-stable operations can be obtained in the usual way from the motivic reduced powers and the Bockstein homomorphism.Comment: This version is very close to the final version accepted to the publication in Publ. IHE