Stalk (sheaf)The stalk of a sheaf is a mathematical construction capturing the behaviour of a sheaf around a given point. Sheaves are defined on open sets, but the underlying topological space consists of points. It is reasonable to attempt to isolate the behavior of a sheaf at a single fixed point of . Conceptually speaking, we do this by looking at small neighborhoods of the point. If we look at a sufficiently small neighborhood of , the behavior of the sheaf on that small neighborhood should be the same as the behavior of at that point.
Perverse sheafThe mathematical term perverse sheaves refers to a certain associated to a topological space X, which may be a real or complex manifold, or a more general topologically stratified space, usually singular. This concept was introduced in the thesis of Zoghman Mebkhout, gaining more popularity after the (independent) work of Joseph Bernstein, Alexander Beilinson, and Pierre Deligne (1982) as a formalisation of the Riemann-Hilbert correspondence, which related the topology of singular spaces (intersection homology of Mark Goresky and Robert MacPherson) and the algebraic theory of differential equations (microlocal calculus and holonomic D-modules of Joseph Bernstein, Masaki Kashiwara and Takahiro Kawai).
November 1918 in Alsace-LorraineNovember 1918 was the period of transition when the region of Alsace-Lorraine passed from German to French sovereignty at the end of World War I. During this month, international events were linked to domestic troubles, particularly the German Revolution. In the wake of the German Revolution, councils of workers and soldiers (Soldaten- und Arbeiterräte) formed in Mulhouse on November 9 and in Colmar and Strasbourg on November 10, in parallel to other such bodies set up in the general revolutionary atmosphere of the expiring Reich and in imitation of the Russian equivalent soviets.
Direct image with compact supportIn mathematics, the direct image with compact (or proper) support is an for sheaves that extends the compactly supported global sections functor to the relative setting. It is one of Grothendieck's six operations. Let f: X → Y be a continuous mapping of locally compact Hausdorff topological spaces, and let Sh(–) denote the of sheaves of abelian groups on a topological space. The direct image with compact (or proper) support is the functor f!: Sh(X) → Sh(Y) that sends a sheaf F on X to the sheaf f!(F) given by the formula f!(F)(U) := {s ∈ F(f −1(U)) | f|supp(s): supp(s) → U is proper} for every open subset U of Y.
Roberto CarifiRoberto Carifi (born 1948 in Pistoia), is an Italian poet, philosopher, and translator, supported since the beginning from Piero Bigongiari, one of the major exponents of Florentine Hermeticism. Considered one of the most important poet and intellectual of his generation he has been influenced by having a very difficult illness to cope with. Since his university years Carifi was attracted by French and German philosophy, in his mature age he also crossed paths with Buddhist, getting influenced for instance in his collections, such as Tibet and The Secret.
Morphism of algebraic varietiesIn algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also regular is called biregular, and the biregular maps are the isomorphisms of algebraic varieties.
Čech cohomologyIn mathematics, specifically algebraic topology, Čech cohomology is a cohomology theory based on the intersection properties of open covers of a topological space. It is named for the mathematician Eduard Čech. Let X be a topological space, and let be an open cover of X. Let denote the nerve of the covering. The idea of Čech cohomology is that, for an open cover consisting of sufficiently small open sets, the resulting simplicial complex should be a good combinatorial model for the space X.
Robert ChaudensonRobert Chaudenson (12 April 1937 – 7 April 2020) was a French linguist. He was a specialist in creole languages and an emeritus professor of linguistics at the University of Provence. He was a widely known author on the subject of creolistics and president of the International Committee of Creole Studies. He was born in Lyon, and died aged 82, just 5 days before his 83rd birthday in Metropolitan France due to complications of COVID-19. 1974. Le lexique du parler créole de la Réunion, 2 vol., Paris: Champion, 1249 p.
Grothendieck topologyIn , a branch of mathematics, a Grothendieck topology is a structure on a category C that makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site. Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology. This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the étale cohomology of a scheme.
