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In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
Séminaire de Géométrie Algébrique du Bois Marie - 1962 - Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux - (SGA 2) (Advanced Studies in Pure Mathematics 2) (in French). Amsterdam: North-Holland Publishing Company. vii+287.
The Éléments de géométrie algébrique (EGA; from French: "Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné) is a rigorous treatise on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques.
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures. Étale cohomology theory can be used to construct ℓ-adic cohomology, which is an example of a Weil cohomology theory in algebraic geometry.
Rigor is a cornerstone quality of mathematics, and can play an important role in preventing mathematics from degenerating into fallacies. well-behaved An object is well-behaved (in contrast with being Pathological ) if it satisfies certain prevailing regularity properties, or if it conforms to mathematical intuition (even though intuition can ...
Pierre Berthelot (French:; 27 January 1943 – 7 December 2023) was a French mathematician at the University of Rennes. He developed crystalline cohomology and rigid cohomology. Berthelot died on 7 December 2023. [1]
An axiom schema is a formula in the metalanguage of an axiomatic system, in which one or more schematic variables appear. These variables, which are metalinguistic constructs, stand for any term or subformula of the system, which may or may not be required to satisfy certain conditions.
The T-schema is often expressed in natural language, but it can be formalized in many-sorted predicate logic or modal logic; such a formalisation is called a T-theory. T-theories form the basis of much fundamental work in philosophical logic , where they are applied in several important controversies in analytic philosophy .