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Abstract: In this Note, we construct for some normal surface X an object of whose homology sheaves are not strictly -invariant. This disproves the -connectivity conjecture of F. Morel. To cite this article: J. Ayoub, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Abstract: Using an inequality for the Weil height on an Abelian extension of the rationals and a theorem of Linnik, we prove a lower bound for the index of the annihilator of the ideal class group of a cyclotomic field. This lower bound is exponential in the degree of the field. To cite this article: F. Amoroso, C. R. Acad. Sci. Paris, Ser. I 342 (2006). [Copyright &y& Elsevier]

Let (X,ω) be a compact complex Hermitian manifold, and let T⩾γ be a d-closed (1,1) almost positive current on X. A variant of Demailly''s regularization-of-currents theorem states that T is the weak limit of a sequence of (1,1)-currents Tm with analytic singularities of coefficient 1/m, lying in the same cohomology class as T, whose Lelong numbers converge to those of T, and with a loss of positivity decaying to zero. We prove that if the (1,1)-form γ is assumed to be closed and C∞, the regularizing currents Tm can be chosen such that Tm⩾γ−C/m for a constant C>0 independent of m. To cite this article: D. Popovici, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]

We show that any binary type II code can be built as a Cortex code where the basis code is the [8,4,4] extended Hamming code. To cite this article: A. Otmani, C. R. Acad. Sci. Paris, Ser. I 336 (2003). [Copyright &y& Elsevier]