Section 9412 026n Algebraic Stacksthe Stacks Project

Understanding section 9412026nalgebraicstacksthestacks project requires examining multiple perspectives and considerations. Section 94.12 (026N): Algebraicstacks—The Stacks project. Our point of view is to try to prove a certain number of the results that follow only assuming that the diagonal of \mathcal {X} be representable by algebraic spaces, and simply add an additional hypothesis wherever this is necessary. The Stacks Project in nLab - ncatlab.org. In addition, the project issued a collection of several more advanced articles which are beyond the current state of the main textbook project: Last revised on October 15, 2024 at 04:55:32. See the history of this page for a list of all contributions to it.

an open source textbook and reference work on algebraic geometry Algebraic stack - Wikipedia. In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Another key aspect involves, section 94.1 (026L): Introduction—The Stacks project.

It's important to note that, this chapter is not an introduction to algebraic stacks. For an informal discussion of algebraic stacks, please take a look at Introducing Algebraic Stacks, Section 105.1. A GUIDE TO THE LITERATURE ON ALGEBRAIC STACKS. We provide an informal guide to useful books and research papers on algebraic stacks. It is undoubtedly incomplete. Any comments, corrections, changes, additions, or suggestions are welcome!

From another angle, short introductory articles. Barbara Fantechi: Stacks for Everybody [Fan01] Dan Edidin: What is a stack? Section 100.4 (04XE): Points of algebraic stacks—The Stacks project. Let $\mathcal {X}$ be an algebraic stack.

Let $K, L$ be two fields and let $p : \mathop {\mathrm {Spec}} (K) \to \mathcal {X}$ and $q : \mathop {\mathrm {Spec}} (L) \to \mathcal {X}$ be morphisms. We say that $p$ and $q$ are equivalent if there exists a field $\Omega $ and a $2$-commutative diagram. Similarly, a MODERN INTRODUCTION TO ALGEBRAIC STACKS.

Recognizing algebraic spaces and Deligne{Mumford stacks. Section 94.13 (03YR): Algebraic stacks and algebraic spaces—The Stacks .... Similarly, in this section we discuss some simple criteria which imply that an algebraic stack is an algebraic space. The main result is that this happens exactly when objects of fibre categories have no nontrivial automorphisms.

This is not a triviality! Before we come to this we first do a sanity check. Index—The Stacks project. 026L This is where we define algebraic stacks and make some very elementary obser-vations.