هندسه جبری هموتوپیک II: دسته‌های هندسی و کاربردها

This is the second part of a series of papers called "HAG", devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, etale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties. This is the second part of a series of papers called “HAG”, devoted to developing the foundations of homotopical algebraic geometry. The authors start by defining and studying generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, étale and smooth morphisms, flat and projective modules, etc. They then use their theory of stacks over model categories to define a general notion of geometric stack over a base symmetric monoidal model category $C$, and prove that this notion satisfies the expected properties. The second part of a series of papers called ""HAG"", devoted to developing the foundations of homotopical algebraic geometry, this work defines and studies generalizations of standard notions of linear algebra in an abstract monoidal model category, such as derivations, etale and smooth morphisms, and flat and projective modules.