Everything about Algebraic stack
Generalization of algebraic spaces or schemes
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. Originally, they were introduced by Alexander Grothendieck to keep track of automorphisms on moduli spaces, a technique which allows for treating these moduli spaces as if their underlying schemes or algebraic spaces are smooth. After Grothendieck developed the general theory of descent, and Giraud the general theory of stacks, the notion of algebraic stacks was defined by Michael Artin. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Algebraic stackA 5-minute orientation
- Skim a recent paper: Cox ring of an algebraic stackInfluential work since 2022
- Pick up a classic book: Algebraic numbers and algebraic functionsThe most-reprinted book on the subject
- Read the landmark paper: Field Validation of Algebraic Equations for Stack and Wind Driven Air Infiltration CalculationsCited 81 times
- Go sideways: Stack (mathematics)A closely related topic
- Go sideways: Glossary of algebraic geometryA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Field Validation of Algebraic Equations for Stack and Wind Driven Air Infiltration Calculations
The Schwartz space of a smooth semi-algebraic stack
Finiteness theorems for the Picard objects of an algebraic stack
Cohomology of the moduli stack of algebraic vector bundles
The Nisnevich motive of an algebraic stack
Permutations Generated by a Depth 2 Stack and an Infinite Stack in Series are Algebraic
Notes on algebraic log stack
Correction to: The Schwartz space of a smooth semi-algebraic stack
🆕 Influential since 2022
📚 Books worth reading
Algebraic numbers and algebraic functionsP. M. Cohn · 1991
Deformation spacesHossein Abbaspour · 2010
Derived L-Adic Categories for Algebraic StacksK. Behrend · 2003
Algèbre locale, multiplicitésJean-Pierre Serre, Pierre Gabriel · 2002
Study in Derived Algebraic Geometry : Volume IIDennis Gaitsgory, Nick Rozenblyum · 2017- 📕Algebraic spaces and stacksMartin C. Olsson · 2016
- 📕Homotopical algebraic geometry IIBertrand Toën · 2008
- 📕On the classification of 2-gerbes and 2-stacksLawrence Breen · 1994
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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