Semipurity of tempered Deligne cohomology

In this paper we define the formal and tempered Deligne cohomology groups, that are obtained by applying the Deligne complex functor to the complexes of formal differential forms and tempered currents respectively. We then prove the existence of a duality between them, a vanishing theorem for the former and a semipurity property for the latter. The motivation of these results comes from the study of covariant arithmetic Chow groups. The semi-purity property of tempered Deligne cohomology implies, in particular, that several definitions of covariant arithmetic Chow groups agree for projective arithmetic varieties

Central orderings in fields of real meromorphic function germs

The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0⊂Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the closure of the set of smooth points of maximal dimension). In the case of germs, the central points are replaced by curves or, more precisely, half branch germs (actually even C∞ branch germs); the dimension of a half branch germ is the dimension of the smallest analytic germ which contains this half germ. An order on K(X0) is said to be centered on a half branch c if the set of its positive elements contains the functions which are positive on c. If Ωe is the set of orders on K(X0) centered on a half branch of dimension e, it is proved that all Ωe (e=1,⋯,d) and Ω∖Ω∗ (with Ω∗=Ω1∪⋯∪Ωd) are dense in Ω. Various other results and applications are given

Central orderings in fields of real meromorphic function germs

The paper deals with orderings in the field K(X0) of meromorphic function germs on an irreducible analytic germ X0⊂Rn0 of dimension d. It is inspired by the theory of central points of real algebraic varieties (the set of central points is the closure of the set of smooth points of maximal dimension). In the case of germs, the central points are replaced by curves or, more precisely, half branch germs (actually even C∞ branch germs); the dimension of a half branch germ is the dimension of the smallest analytic germ which contains this half germ. An order on K(X0) is said to be centered on a half branch c if the set of its positive elements contains the functions which are positive on c. If Ωe is the set of orders on K(X0) centered on a half branch of dimension e, it is proved that all Ωe (e=1,⋯,d) and Ω∖Ω∗ (with Ω∗=Ω1∪⋯∪Ωd) are dense in Ω. Various other results and applications are given

Minimal generation of basic open semianalytic sets.

Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu

Nestin as a diagnostic and prognostic marker for combined hepatocellular-cholangiocarcinoma.

Combined Hepatocellular-Cholangiocarcinoma (cHCC-CCA) is a rare primary liver cancer (PLC) associated with a poor prognosis. Given the challenges in its identification and its clinical implications, biomarkers are critically needed. We aimed to investigate the diagnostic and prognostic value of the immunohistochemical expression of Nestin, a progenitor cell marker, in a large multicentric series of PLC. We collected 461 cHCC-CCA samples from 32 different clinical centers. Control cases included 368 hepatocellular carcinomas (HCC) and 221 intrahepatic cholangiocarcinomas (ICCA). Nestin immunohistochemistry was performed on whole tumor sections. Diagnostic and prognostic performances of Nestin expression were determined using receiver operating characteristic curves and cox regression modeling. Nestin was able to distinguish cHCC-CCA from HCC with AUC of 0.85 and 0.86 on surgical and biopsy samples, respectively. Performance was lower for the distinction of cHCC-CCA from ICCA (AUC of 0.59 and 0.60). Nestin, however, showed a high prognostic value, allowing identification of the subset of cHCC-CCA ("Nestin High", >30% neoplastic cells with positive staining) associated with the worst clinical outcome (shorter disease-free and overall survival) after surgical resection and liver transplantation, as well as when assessment was performed on biopsies. We show in different clinical settings that Nestin has a diagnostic value and that it is a useful biomarker to identify the subset of cHCC-CCA associated with the worst clinical outcome. Nestin immunohistochemistry may be used to refine risk stratification and improve treatment allocation for patients with this highly aggressive malignancy. Combined Hepatocellular-Cholangiocarcinoma (cHCC-CCA) is a rare primary liver cancer (PLC) that lacks robust tissue biomarkers. We show in different clinical settings that Nestin immunohistochemical staining has a diagnostic value and is a useful biomarker to identify the subset of cHCC-CCA associated with the worst clinical outcome. Nestin immunohistochemistry may be used to refine risk stratification and improve treatment allocation for patients with this highly aggressive malignancy