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stacks-properties.pdf
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🔗 Source: math.columbia.edu
📊 Size: 435 KB
📄 Pages: 33 pages
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The chapter discusses properties of algebraic stacks, including morphisms representable by algebraic spaces, points of algebraic stacks, surjective morphisms, quasi-compact algebraic stacks, and dimension of a stack. It establishes conventions for algebraic stacks, algebraic spaces, and schemes, and introduces notation for products and fibre products. The chapter also proves lemmas about morphisms representable by algebraic spaces, including a result that a morphism is representable by algebraic spaces if it is so after a base change by a flat, locally finitely presented, surjective morphism. Additionally, it discusses properties of morphisms of algebraic stacks, such as being surjective, smooth, or étale, and how these properties are preserved under base change and composition.

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The chapter discusses properties of algebraic stacks, including morphisms representable by algebraic spaces, points of algebraic stacks, surjective morphisms,...

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  • File Format: PDF
  • File Size: 435 KB
  • Pages: 33
  • Language: EN
  • Total Downloads: 114
  • Last Updated: 1 week ago

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