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Séminaire De Géométrie Algébrique Du Bois Marie
In mathematics, the (''SGA''; from French: "Seminar on Algebraic Geometry of Bois Marie") was an influential seminar run by French mathematician Alexander Grothendieck. It was a unique phenomenon of research and publication outside of the main mathematical journals that ran from 1960 to 1969 at the (IHÉS) near Paris. (The name came from the small wood on the estate in Bures-sur-Yvette where the IHÉS was located from 1962.) The seminar notes were eventually published in twelve volumes, all except one in the Springer Lecture Notes in Mathematics series. Style The material has a reputation of being hard to read for a number of reasons. More elementary or foundational parts were relegated to the EGA series of Grothendieck and Jean Dieudonné, causing long strings of logical dependencies in the statements. The style is very abstract and makes heavy use of category theory. Moreover, an attempt was made to achieve maximally general statements, while assuming that the reader is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lefschetz Theorem
Solomon Lefschetz (; 3 September 1884 – 5 October 1972) was a Russian-born American mathematician who did fundamental work on algebraic topology, its applications to algebraic geometry, and the theory of non-linear ordinary differential equations. Life He was born in Moscow, the son of Alexander Lefschetz and his wife Sarah or Vera Lifschitz, Jewish traders who used to travel around Europe and the Middle East (they held Ottoman passports). Shortly thereafter, the family moved to Paris. He was educated there in engineering at the École Centrale Paris, but emigrated to the US in 1905. He was badly injured in an industrial accident in 1907, losing both hands. He moved towards mathematics, receiving a Ph.D. in algebraic geometry from Clark University in Worcester, Massachusetts in 1911. He then took positions in University of Nebraska and University of Kansas, moving to Princeton University in 1924, where he was soon given a permanent position. He remained there until 1953. In t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
External Links
An internal link is a type of hyperlink on a web page to another page or resource, such as an image or document, on the same website or domain. It is the opposite of an external link, a link that directs a user to content that is outside its domain. Hyperlinks are considered either "external" or "internal" depending on their target or destination. Generally, a link to a page outside the same domain or website is considered external, whereas one that points at another section of the same web page or to another page of the same website or domain is considered internal. Both internal and external links allow users of the website to navigate to another web page or resource. These definitions become clouded, however, when the same organization operates multiple domains functioning as a single web experience, e.g. when a secure commerce website is used for purchasing things displayed on a non-secure website. In these cases, links that are "external" by the above definition can conce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Société Mathématique De France
Groupe Lactalis S.A. (doing business as Lactalis) is a French multinational dairy products corporation, owned by the Besnier family and based in Laval, Mayenne, France. The company's former name was Besnier S.A. Lactalis is the largest dairy products group in the world, and is the second largest food products group in France, behind Danone. It owns brands such as Parmalat, Président, Kraft Natural Cheese, Siggi's Dairy, Skånemejerier, Rachel's Organic, and Stonyfield Farm. History André Besnier started a small cheesemaking company in 1933 and launched its '' Président'' brand of Camembert in 1968. In 1990, it acquired Group Bridel (2,300 employees, 10 factories, fourth-largest French dairy group) with a presence in 60 countries. In 1992, it acquired United States cheese company Sorrento. In 1999, ''la société Besnier'' became ''le groupe Lactalis'' owned by Belgian holding company BSA International SA. In 2006, they bought Italian group Galbani, and in 2008, bough ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latices are found in nature, but synthetic latices are common as well. In nature, latex is found as a wikt:milky, milky fluid, which is present in 10% of all flowering plants (angiosperms) and in some Mushroom, mushrooms (especially species of ''Lactarius''). It is a complex emulsion that coagulation, coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, Vegetable oil, oils, tannins, resins, and Natural gum, gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as Antipredator adaptation, defense against Herbivore, herbivores and Fungivore, fungivores.Taskirawati, I. and Tuno, N., 2016Fungal defense against mycophagy in milk caps ''Science Report Kanazaw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IBM Selectric Typewriter
The IBM Selectric (a portmanteau of "selective" and "electric") was a highly successful line of electric typewriters introduced by IBM on 31 July 1961. Instead of the "basket" of individual typebars that swung up to strike the ribbon and page in a typical typewriter of the period, the Selectric had a chrome-plated plastic "element" (frequently called a "typeball", or less formally, a "golf ball") that rotated and tilted to the correct position before striking the paper. The element could be easily interchanged to use different fonts within the same document typed on the same typewriter, resurrecting a capability which had been pioneered by typewriters such as the Hammond and Blickensderfer in the late 19th century. The Selectric also replaced the traditional typewriter's horizontally moving carriage with a roller (platen) that turned to advance the paper vertically while the typeball and ribbon mechanism moved horizontally across the paper. The Selectric mechanism was notable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystalline Cohomology
In mathematics, crystalline cohomology is a Weil cohomology theory for schemes ''X'' over a base field ''k''. Its values ''H''''n''(''X''/''W'') are modules over the ring ''W'' of Witt vectors over ''k''. It was introduced by and developed by . Crystalline cohomology is partly inspired by the ''p''-adic proof in of part of the Weil conjectures and is closely related to the algebraic version of de Rham cohomology that was introduced by Grothendieck (1963). Roughly speaking, crystalline cohomology of a variety ''X'' in characteristic ''p'' is the de Rham cohomology of a smooth lift of ''X'' to characteristic 0, while de Rham cohomology of ''X'' is the crystalline cohomology reduced mod ''p'' (after taking into account higher ''Tor''s). The idea of crystalline cohomology, roughly, is to replace the Zariski open sets of a scheme by infinitesimal thickenings of Zariski open sets with divided power structures. The motivation for this is that it can then be calculated by tak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Berthelot
Pierre Berthelot (; 27 January 1943 – 7 December 2023) was a French mathematician at the University of Rennes. He developed crystalline cohomology and rigid cohomology. Publications *Berthelot, Pierre ''Cohomologie cristalline des schémas de caractéristique p>0.'' Lecture Notes in Mathematics, Vol. 407. Springer-Verlag, Berlin-New York, 1974. 604 pp. *Berthelot, Pierre; Ogus, Arthur ''Notes on crystalline cohomology.'' Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1978. vi+243 pp. References Home pageof Pierre Berthelot * External links Author profilein the database zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ... 1943 births 2023 deaths École Normale Supérieure alumni Algebraic geometers 20th-century French mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monodromy
In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity. As the name implies, the fundamental meaning of ''monodromy'' comes from "running round singly". It is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions we may wish to define fail to be ''single-valued'' as we "run round" a path encircling a singularity. The failure of monodromy can be measured by defining a monodromy group: a group of transformations acting on the data that encodes what happens as we "run round" in one dimension. Lack of monodromy is sometimes called ''polydromy''. Definition Let X be a connected and locally connected based topological space with base point x, and let p: \tilde \to X be a covering with fiber F = p^(x). For a loop \gamma: , 1\to X based at x, denote a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riemann–Roch Theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus ''g'', in a way that can be carried over into purely algebraic settings. Initially proved as Riemann's inequality by , the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student . It was later generalized to algebraic curves, to higher-dimensional varieties and beyond. Preliminary notions A Riemann surface X is a topological space that is locally homeomorphic to an open subset of \Complex, the set of complex numbers. In addition, the transition maps between these open subsets are required to be holomorphic. The latter condition allows one to transfer the notions and methods of c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection Theory
In mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory more quickly reached a definitive form. There is yet an ongoing development of intersection theory. Currently the main focus is on: virtual fundamental cycles, quantum intersection rings, Gromov–Witten theory and the extension of intersection theory from schemes to stacks. Topological intersection form For a connected oriented manifold M of dimension 2n the intersection form is defined on the n-th cohomology group (what is usually called the 'middle dimension') by the evaluation of the cup product on the fundamental class /math> in H_(M,\partial M). Stated precisely, there is a bilinear form :\lambda_M \colon H^n(M,\partial M) \times H^n(M,\partial M)\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
L-function
In mathematics, an ''L''-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects. An ''L''-series is a Dirichlet series, usually convergent on a half-plane, that may give rise to an ''L''-function via analytic continuation. The Riemann zeta function is an example of an ''L''-function, and some important conjectures involving ''L''-functions are the Riemann hypothesis and its generalizations. The theory of ''L''-functions has become a very substantial, and still largely conjectural, part of contemporary analytic number theory. In it, broad generalisations of the Riemann zeta function and the ''L''-series for a Dirichlet character are constructed, and their general properties, in most cases still out of reach of proof, are set out in a systematic way. Because of the Euler product formula there is a deep connection between ''L''-functions and the theory of prime numbers. The mathematical field tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
