Schéma (géométrie algébrique)En mathématiques, les schémas sont les objets de base de la géométrie algébrique, généralisant la notion de variété algébrique de plusieurs façons, telles que la prise en compte des multiplicités, l'unicité des points génériques et le fait d'autoriser des équations à coefficients dans un anneau commutatif quelconque.
Group schemeIn mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Group schemes arise naturally as symmetries of schemes, and they generalize algebraic groups, in the sense that all algebraic groups have group scheme structure, but group schemes are not necessarily connected, smooth, or defined over a field. This extra generality allows one to study richer infinitesimal structures, and this can help one to understand and answer questions of arithmetic significance.
Hilbert schemeIn algebraic geometry, a branch of mathematics, a Hilbert scheme is a scheme that is the parameter space for the closed subschemes of some projective space (or a more general projective scheme), refining the Chow variety. The Hilbert scheme is a disjoint union of projective subschemes corresponding to Hilbert polynomials. The basic theory of Hilbert schemes was developed by . Hironaka's example shows that non-projective varieties need not have Hilbert schemes.
Fiber product of schemesIn mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction. It has many interpretations and special cases. For example, the fiber product describes how an algebraic variety over one field determines a variety over a bigger field, or the pullback of a family of varieties, or a fiber of a family of varieties. Base change is a closely related notion. The of schemes is a broad setting for algebraic geometry.
Formal schemeIn mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Unlike an ordinary scheme, a formal scheme includes infinitesimal data that, in effect, points in a direction off of the scheme. For this reason, formal schemes frequently appear in topics such as deformation theory. But the concept is also used to prove a theorem such as the theorem on formal functions, which is used to deduce theorems of interest for usual schemes.
Derived schemeIn algebraic geometry, a derived scheme is a pair consisting of a topological space X and a sheaf either of simplicial commutative rings or of commutative ring spectra on X such that (1) the pair is a scheme and (2) is a quasi-coherent -module. The notion gives a homotopy-theoretic generalization of a scheme. A derived stack is a stacky generalization of a derived scheme. Over a field of characteristic zero, the theory is closely related to that of a differential graded scheme.
Cycloaddition 1,3-dipolaireLa cycloaddition 1,3-dipolaire, aussi connue sous le nom de cycloaddition de Huisgen ou réaction de Huisgen est une réaction en chimie organique appartenant à la grande famille des cycloadditions péricycliques concertées. C'est une réaction entre un 1,3-dipôle et un dipolairophile, la plupart du temps un alcène substitué, pour former un cycle à cinq atomes. Rolf Huisgen fut le premier à effectuer des recherches sur cette réaction en variant les 1,3-dipôles et à considérer son importance dans la synthèse d'hétérocycles à cinq atomes.
StéréodescripteurIn chemical nomenclature, a descriptor is a notational prefix placed before the systematic substance name, which describes the configuration or the stereochemistry of the molecule. Some listed descriptors are only of historical interest and should not be used in publications anymore as they do not correspond with the modern recommendations of the IUPAC. Stereodescriptors are often used in combination with locants to clearly identify a chemical structure unambiguously.
Chimie clickDans le domaine de la synthèse chimique, la chimie clic, ou chimie click (click chemistry en anglais ou plus communément tagging) est une classe de réactions chimiques biocompatibles utilisées pour joindre à un substrat choisi une biomolécule spécifique (le click peut évoquer le bruit imaginaire d'un clipsage d'une molécule sur l'autre).
Indice d'octaneL'indice d'octane mesure la résistance à l'auto-allumage (allumage sans intervention de la bougie) d'un carburant utilisé dans un moteur à allumage commandé. Ce carburant est très généralement l'essence. On parle assez souvent improprement de capacité antidétonante du carburant pour un carburant d'indice d'octane élevé, un carburant ayant tendance à l'auto-allumage pouvant dans certains cas transiter à la détonation.
