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40 relations: ADE classification, Algebraic curve, Algebraic number field, André Néron, Base change theorems, Birkhäuser, Cartan matrix, Complex manifold, Conjugacy class, Determinant, Differentiable manifold, Dolgachev surface, Dynkin diagram, Elliptic curve, Enriques surface, Enriques–Kodaira classification, F-theory, Genus (mathematics), Homology (mathematics), J-invariant, Kodaira dimension, Kodaira surface, Kunihiko Kodaira, Mathematics, Monodromy, Mordell–Weil theorem, Morphism, Néron model, Potential good reduction, Proper morphism, Publications Mathématiques de l'IHÉS, Regular scheme, Section (fiber bundle), Shioda modular surface, Smooth scheme, Springer Science+Business Media, String theory, Tate's algorithm, Zero matrix, 4-manifold.
ADE classification
In mathematics, the ADE classification (originally A-D-E classifications) is a situation where certain kinds of objects are in correspondence with simply laced Dynkin diagrams.
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Algebraic curve
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
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Algebraic number field
In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
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André Néron
André Néron (November 30, 1922, La Clayette, France – April 6, 1985, Paris, France) was a French mathematician at the Université de Poitiers who worked on elliptic curves and Abelian varieties.
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Base change theorems
In mathematics, the base change theorems relate the direct image and the pull-back of sheaves.
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Birkhäuser
Birkhäuser is a former Swiss publisher founded in 1879 by Emil Birkhäuser.
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Cartan matrix
In mathematics, the term Cartan matrix has three meanings.
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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Differentiable manifold
In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.
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Dolgachev surface
In mathematics, Dolgachev surfaces are certain simply connected elliptic surfaces, introduced by.
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Dynkin diagram
In the mathematical field of Lie theory, a Dynkin diagram, named for Eugene Dynkin, is a type of graph with some edges doubled or tripled (drawn as a double or triple line).
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Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
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Enriques surface
In mathematics, Enriques surfaces are algebraic surfaces such that the irregularity q.
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Enriques–Kodaira classification
In mathematics, the Enriques–Kodaira classification is a classification of compact complex surfaces into ten classes.
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F-theory
F-theory is a branch of string theory developed by Cumrun Vafa.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Homology (mathematics)
In mathematics, homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
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J-invariant
In mathematics, Felix Klein's j-invariant or j function, regarded as a function of a complex variable τ, is a modular function of weight zero for defined on the upper half-plane of complex numbers.
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Kodaira dimension
In algebraic geometry, the Kodaira dimension κ(X) (or canonical dimension) measures the size of the canonical model of a projective variety X. Igor Shafarevich introduced an important numerical invariant of surfaces with the notation κ in the seminar Shafarevich 1965.
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Kodaira surface
In mathematics, a Kodaira surface is a compact complex surface of Kodaira dimension 0 and odd first Betti number.
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Kunihiko Kodaira
was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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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.
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Mordell–Weil theorem
In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A(K) of ''K''-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group.
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Morphism
In mathematics, a morphism is a structure-preserving map from one mathematical structure to another one of the same type.
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Néron model
In algebraic geometry, the Néron model (or Néron minimal model, or minimal model) for an abelian variety AK defined over the field of fractions K of a Dedekind domain R is the "push-forward" of AK from Spec(K) to Spec(R), in other words the "best possible" group scheme AR defined over R corresponding to AK.
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Potential good reduction
In mathematics, potential good reduction is a property of the reduction modulo a prime or, more generally, prime ideal, of an algebraic variety.
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Proper morphism
In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.
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Publications Mathématiques de l'IHÉS
Publications Mathématiques de l'IHÉS is a mathematical journal.
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Regular scheme
In algebraic geometry, a regular scheme is a scheme whose local rings are regular everywhere.
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Section (fiber bundle)
In the mathematical field of topology, a section (or cross section) of a fiber bundle E is a continuous right inverse of the projection function \pi.
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Shioda modular surface
In mathematics, a Shioda modular surface is one of the elliptic surfaces studied by.
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Smooth scheme
In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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String theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings.
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Tate's algorithm
In the theory of elliptic curves, Tate's algorithm takes as input an integral model of an elliptic curve E over \mathbb, or more generally an algebraic number field, and a prime or prime ideal p. It returns the exponent fp of p in the conductor of E, the type of reduction at p, the local index where E^0(\mathbb_p) is the group of \mathbb_p-points whose reduction mod p is a non-singular point.
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Zero matrix
In mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero.
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4-manifold
In mathematics, a 4-manifold is a 4-dimensional topological manifold.
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Elliptic fibration, Elliptic surfaces, Logarithmic transformation, Quasi-elliptic surface.
References
[1] https://en.wikipedia.org/wiki/Elliptic_surface
