A going down theorem for Grothendieck Chow motives

Let X be a geometrically split, geometrically irreducible variety over a field F satisfying Rost nilpotence principle. Consider a field extension E/F and a finite field K. We provide in this note a motivic tool giving sufficient conditions for so-called outer motives of direct summands of the Chow motive of X_E with coefficients in K to be lifted to the base field. This going down result has been used S. Garibaldi, V. Petrov and N. Semenov to give a complete classification of the motivic decompositions of projective homogeneous varieties of inner type E_6 and to answer a conjecture of Rost and Springer.Comment: Final version of the manuscrip

Classification of upper motives of algebraic groups of inner type A_n

Let A, A' be two central simple algebras over a field F and \mathbb{F} be a finite field of characteristic p. We prove that the upper indecomposable direct summands of the motives of two anisotropic varieties of flags of right ideals X(d_1,...,d_k;A) and X(d'_1,...,d'_s;A') with coefficients in \mathbb{F} are isomorphic if and only if the p-adic valuations of gcd(d_1,...,d_k) and gcd(d'_1,..,d'_s) are equal and the classes of the p-primary components A_p and A'_p of A and A' generate the same group in the Brauer group of F. This result leads to a surprising dichotomy between upper motives of absolutely simple adjoint algebraic groups of inner type A_

Motivic decompositions of projective homogeneous varieties and change of coefficients

We prove that under some assumptions on an algebraic group $G$, indecomposable direct summands of the motive of a projective $G$-homogeneous variety with coefficients in $\mathbb{F}_p$ remain indecomposable if the ring of coefficients is any field of characteristic $p$. In particular for any projective $G$-homogeneous variety $X$, the decomposition of the motive of $X$ in a direct sum of indecomposable motives with coefficients in any finite field of characteristic $p$ corresponds to the decomposition of the motive of $X$ with coefficients in $\mathbb{F}_p$. We also construct a counterexample to this result in the case where $G$ is arbitrary

The Development of Regulatory Standards for Gene Therapy in the European Union

This note examines the EU\u27s efforts to regulate gene therapy, considering the Union\u27s resolve to establish scientifically, economically, and morally sound parameters acceptable to its varied constituency. This includes discussion of legal and ethical considerations, biotechnology goals in the EU, and EU-wide uniform regulations

On Sloane's persistence problem

We investigate the so-called persistence problem of Sloane, exploiting connections with the dynamics of circle maps and the ergodic theory of $\mathbb{Z}^d$ actions. We also formulate a conjecture concerning the asymptotic distribution of digits in long products of finitely many primes whose truth would, in particular, solve the persistence problem. The heuristics that we propose to complement our numerical studies can be thought in terms of a simple model in statistical mechanics.Comment: 5 figure

A laboratory method to evaluate the sensitivity of Colletotrichum musea to post harvest fungicides

Introduction. Ce protocole vise à détecter et évaluer des variations de sensibilité dans des populations de Colletotrichum musae vis-à-vis des fongicides actuellement utilisés pour le contrôle des maladies de conservation des bananes. Le principe, les principaux avantages, le matériel végétal de départ, le temps nécessaire et les résultats attendus de la méthode sont présentés. Matériel et méthodes. Le matériel de laboratoire nécessaire, et le détail des douze étapes du protocole réalisé pour l'échantillonnage des bananes et le développement des lésions dues à l'anthracnose, la préparation des boites de milieu gélosé (agar), les isolements monospores, les tests de germination et l'analyse des données sont décrits. De possibles problèmes sont évoqués. Nous obtenons (a) pour les produits antimitotiques, le pourcentage de souches résistantes dans la population analysée ; (b) pour des fongicides inhibiteurs de la biosynthèse des stérols (SBI), la variation et la distribution de la sensibilité des isolats dans la population analysée en fonction de la réduction de leur croissance radiale, imputable au fongicide. (Résumé d'auteur