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Pseudoreductive groups
 Series: New Mathematical Monographs (No. 17) (to appear). 8 LIOR BARYSOROKER AND NGUYÊÑ DUY TÂN
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Twisted equivariant Ktheory with complex coefficients
, 2008
"... Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space ..."
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Cited by 70 (7 self)
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Using a global version of the equivariant Chern character, we describe an effective method for computing the complexified twisted equivariant Ktheory of a space
Complete intersection dimension
"... A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CIdimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CIdimension, providing the first class of modules of (possibly) ..."
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Cited by 67 (11 self)
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A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CIdimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CIdimension, providing the first class of modules of (possibly)
Using stacks to impose tangency conditions on curves
 math.AG/0210398. [Ch1] [Ch2] [Co87] [DM69] [FSZ] [Gr68] [Ha83
"... From a scheme Y, an effective Cartier divisor D ⊂ Y, and a positive integer r, we define a stack YD,r and work out some of its basic properties. The most important of these relates morphisms from a curve C into YD,r to morphisms from C into Y such that the order of contact of C with D is a multiple ..."
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Cited by 66 (5 self)
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From a scheme Y, an effective Cartier divisor D ⊂ Y, and a positive integer r, we define a stack YD,r and work out some of its basic properties. The most important of these relates morphisms from a curve C into YD,r to morphisms from C into Y such that the order of contact of C with D is a multiple of r at each point. This is a foundational paper whose results will be applied to the enumerative geometry of curves with tangency conditions in a future paper. 1
Local cohomology and support for triangulated categories
, 2007
"... We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Suitably ..."
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Cited by 59 (19 self)
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We propose a new method for defining a notion of support for objects in any compactly generated triangulated category admitting small coproducts. This approach is based on a construction of local cohomology functors on triangulated categories, with respect to a central ring of operators. Suitably specialized one recovers, for example, the theory for commutative noetherian rings due to Foxby and Neeman, the theory of Avramov and Buchweitz for complete intersection local rings, and varieties for representations of finite groups according to Benson, Carlson, and Rickard. We give explicit examples of objects whose triangulated support and cohomological support differ. In the case of group representations, this leads to a counterexample to a conjecture of Benson.
Irreducible components of rigid spaces
, 1998
"... This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field k. We prove the excellence of the local rings on rigid spaces over k. This is used to prove the standard existence theorems and to show compatibility with the notion of irre ..."
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Cited by 55 (2 self)
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(Show Context)
This paper lays the foundations for the global theory of irreducible components of rigid analytic spaces over a complete field k. We prove the excellence of the local rings on rigid spaces over k. This is used to prove the standard existence theorems and to show compatibility with the notion of irreducible components for schemes and formal schemes. Behavior with respect to extension of the base field is also studied. It is often necessary to augment schemetheoretic techniques with other algebraic and geometric arguments. COMPONANTES IRRÉDUCTIBLE D’ESPACES RIGIDES Cet article donne les fondements de la théorie globale des composantes irréductibles d’espaces analytiques rigides sur un corps complet k. Nous prouvons l’excellence d’anneaux locaux sur les espaces rigides sur k. De là, nous prouvons les théorèmes standards d’existence et nous montrons la compatibilité avec les notions des composantes irréductibles pour les schémas et les schémas formels. Le comportement par rapport à l’extension de corps base est aussi étudié. Il est souvent nécessaire de compléter les techniques de théorie des schémas par d’autres arguments algébriques et géométriques.