Abstract: One says a scheme, or an algebraic stack, has the resolution property if every coherent sheaf is the quotient of a locally free sheaf. Although this is a fundamental and widely used property in algebraic geometry, it is still poorly understood. After giving the appropriate definitions, we will explain the two most important sources of non-examples: (1) affine group schemes G/S which cannot be embedded into GL_n but which are forms of embeddable group schemes, and (2) cohomological Brauer classes which are not represented by Azumaya algebras. After describing a new way to construct non-trivial vector bundles on schemes and stacks, we introduce the notion of an R-unipotent morphism and characterize it geometrically. We will then present a surprising local to global principle: a locally R-unipotent morphism over a base with enough line bundles is globally R-unipotent. To conclude, we will explain why the unipotent analogues of (1) and (2) above cannot occur.
Il seminario sarà presentato in presenza nell'aula M1. Per informazioni si può contattare gli organizzatori all'Link Link identifier #identifier__137819-1email amos.turchet@uniroma3.it.
Seguibile via Teams a questo Link identifier #identifier__133050-2Link
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