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Ravi D. Vakil (born February 22, 1970) is a Canadian-American mathematician working in algebraic geometry. He is the current president of the American Mathematical Society . Education and career
Hartshorne, Robin (1977), Algebraic Geometry, Graduate Texts in Mathematics, vol. 52, New York: Springer-Verlag, ISBN 978-0-387-90244-9, MR 0463157; Milne, Review of Algebraic Geometry at Algebraic Groups: The theory of group schemes of finite type over a field. Vakil, Ravi (30 December 2014), Foundations of Algebraic Geometry (PDF) (Draft ed.)
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In mathematics, more specifically abstract algebra and commutative algebra, Nakayama's lemma — also known as the Krull–Azumaya theorem [1] — governs the interaction between the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules.
Notably, for a Hausdorff space, the algebra of scalars (the bounded continuous functions on the space, being analogous to regular functions) is a commutative C*-algebra, with the space being recovered as a topological space from of the algebra of scalars, indeed functorially so; this is the content of the Banach–Stone theorem. Indeed, any ...
Download as PDF; Printable version; In other projects Wikidata item; ... Test ideals are used in the study of singularities in algebraic geometry in positive ...
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).
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials ; the modern approach generalizes this in a few different aspects.