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Sheaves on Artin stacks
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Martin Olsson
Published/Copyright:
March 12, 2007
Abstract
We develop a theory of quasi-coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of Laumon and Moret-Bailly. We study basic cohomological properties of such sheaves, and prove stack-theoretic versions of Grothendieck's Fundamental Theorem for proper morphisms, Grothendieck's Existence Theorem, Zariski's Connectedness Theorem, as well as finiteness theorems for proper push forwards of coherent and constructible sheaves. We also explain how to define a derived pullback functor which enables one to carry through the construction of a cotangent complex for a morphism of algebraic stacks due to Laumon and Moret-Bailly.
Received: 2005-03-20
Revised: 2005-11-02
Published Online: 2007-03-12
Published in Print: 2007-03-27
© Walter de Gruyter
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Articles in the same Issue
- Massey products and ideal class groups
- Purity of exponential sums on 𝔸n, II
- Sheaves on Artin stacks
- Levi umbilical surfaces in complex space
- A realization of the Hecke algebra on the space of period functions for Γ0 (n)
- The 5-canonical system on 3-folds of general type
- On Spin L-functions for GSO10
- Nonexistence of higher codimensional Levi-flat CR manifolds in symmetric spaces
