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Crystal (mathematics)

Index Crystal (mathematics)

In mathematics, crystals are cartesian sections of certain fibered categories. [1]

11 relations: Coherent sheaf, Crystalline cohomology, Dieudonné module, F-crystal, Fibred category, Module (mathematics), P-adic number, Princeton University Press, Scheme (mathematics), Sheaf (mathematics), Springer Science+Business Media.

Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space.

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Crystalline cohomology

In mathematics, crystalline cohomology is a Weil cohomology theory for schemes X over a base field k. Its values Hn(X/W) are modules over the ring W of Witt vectors over k. It was introduced by and developed by.

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Dieudonné module

In mathematics, a Dieudonné module introduced by, is a module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius and Verschiebung operators.

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F-crystal

In algebraic geometry, F-crystals are objects introduced by that capture some of the structure of crystalline cohomology groups.

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Fibred category

Fibred categories (or fibered categories) are abstract entities in mathematics used to provide a general framework for descent theory.

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Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

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P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

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Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

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Scheme (mathematics)

In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.

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Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.

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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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Crystal (geometry).

References

[1] https://en.wikipedia.org/wiki/Crystal_(mathematics)

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