The nilpotence conjecture in K-theory of toric varieties
نویسندگان
چکیده
منابع مشابه
The Nilpotence Conjecture in K-theory of Toric Varieties
It is shown that all nontrivial elements in higher K-groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorphisms. This is a higher analog of the triviality of vector bundles on affine toric varieties. 1. Statement of the main result The nilpotence conjecture in K-theory of toric varieties, treated in our previous works, asser...
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The main result of the work “The nilpotence conjecture in K-theory of toric varieties” is extended to all coefficient fields of characteristic 0, thus covering the class of genuine toric varieties. 1. The statement Let R be a (commutative) regular ring, M be arbitrary commutative, cancellative, torsion free monoid without nontrivial units, and i be a nonnegative integral number. The nilpotence ...
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Recent advances in computational techniques for K-theory allow us to describe the K-theory of toric varieties in terms of the K-theory of fields and simple cohomological data.
متن کاملThe Equivariant K - Theory of Toric Varieties
This paper contains two results concerning the equivariant K-theory of toric varieties. The first is a formula for the equivariant K-groups of an arbitrary affine toric variety, generalizing the known formula for smooth ones. In fact, this result is established in a more general context, involving the K-theory of graded projective modules. The second result is a new proof of a theorem due to Ve...
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Let X be a simplicial, quasi-projective toric variety. The goal of this article is to show that the groups Gi(X) of Ktheory of coherent sheaves and Ki(X) of vector bundles are rationally isomorphic. The case i = 0 answers a question of Brion and Vergne.
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2005
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-004-0410-3