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In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory , and to construct fine moduli stacks when fine moduli spaces do not exist.
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them".
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory.Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves, and the moduli stack of elliptic curves.
As a matter of fact, the description is formally analogous, and nearly identical, to the description of the homology groups of a chain complex – and it would seem therefore that that stacks (more specifically, Gr-stacks) are in a sense the closest possible non-commutative generalization of chain complexes, the homology groups of the chain complex becoming the homotopy groups of the “non ...
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
In algebraic geometry, a derived stack is, roughly, a stack together with a sheaf of commutative ring spectra. [1] It generalizes a derived scheme . Derived stacks are the "spaces" studied in derived algebraic geometry .
MathOverflow is a mathematics question-and-answer (Q&A) website, which serves as an online community of mathematicians. It allows users to ask questions, submit answers, and rate both, all while getting merit points for their activities. [1] It is a part of the Stack Exchange Network, but distinct from math.stackexchange.com.
Stack (geology), a large vertical column of rock in the sea; Stack (mathematics), a sheaf that takes values in categories rather than sets; Algebraic stack, a special kind of stack commonly used in algebraic geometry Stacks Project, an open source collaborative mathematics textbook writing project