992 resultados para Grothendieck, Alexander


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"Vegeu el resum a l'inici del document del fitxer adjunt."

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This article presents a way to associate a Grothendieck site structure to a category endowed with a unique factorisation system of its arrows. In particular this recovers the Zariski and Etale topologies and others related to Voevodsky's cd-structures. As unique factorisation systems are also frequent outside algebraic geometry, the same construction applies to some new contexts, where it is related with known structures dened otherwise. The paper details algebraic geometrical situations and sketches only the other contexts.

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We study the singular Bott-Chern classes introduced by Bismut, Gillet and Soulé. Singular Bott-Chern classes are the main ingredient to define direct images for closed immersions in arithmetic K-theory. In this paper we give an axiomatic definition of a theory of singular Bott-Chern classes, study their properties, and classify all possible theories of this kind. We identify the theory defined by Bismut, Gillet and Soulé as the only one that satisfies the additional condition of being homogeneous. We include a proof of the arithmetic Grothendieck-Riemann-Roch theorem for closed immersions that generalizes a result of Bismut, Gillet and Soulé and was already proved by Zha. This result can be combined with the arithmetic Grothendieck-Riemann-Roch theorem for submersions to extend this theorem to arbitrary projective morphisms. As a byproduct of this study we obtain two results of independent interest. First, we prove a Poincaré lemma for the complex of currents with fixed wave front set, and second we prove that certain direct images of Bott-Chern classes are closed.

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Ultrastructural aspects of spermatogenesis, spermiogenesis and of the mature spermatozoon of a microcotylid monogenean Metamicrocotyla macracantha parasite from Mugil liza, are described. The irregularly-shaped spermatogonia divides by successive mitoses, forming the primary spermatocytes, identified by the presence of synaptonemal complexes in their nuclei. The spermatids formed by meiotic cell divisions of the secondary spermatocytes, differentiate into a mature spermatozoon. Cross sections of the head and the middle region of mature spermatozoa show the nucleus with strong condensed chromatin, the mitochondria with short cristae, peripheral microtubules and two axonemes with a 9+1 pattern, confirming the characteristics of this genus.