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Polytopes and K-theory
Winfried Bruns, Joseph Gubeladze
This is an overview of results from our experiment of merging two seemingly unrelated disciplines - higher algebraic K-theory of rings and the theory of lattice polytopes. The usua…
The coefficient field in the nilpotence conjecture for toric varieties
Joseph Gubeladze
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 genui…
The nilpotence conjecture in K-theory of toric varieties
Joseph Gubeladze
It is shown that all nontrivial elements in higher -groups of toric varieties over a class of regular rings are annihilated by iterations of the natural Frobenius type endomorph…
Higher polyhedral K-groups
Winfried Bruns, Joseph Gubeladze
We define higher polyhedral K-groups for commutative rings, starting from the stable groups of elementary automorphisms of polyhedral algebras. Both Volodin's theory and Quillen's…
Polyhedral K_2
Winfried Bruns, Joseph Gubeladze
Using elementary graded automorphisms of polytopal algebras (essentially the coordinate rings of projective toric varieties) polyhedral versions of the group of elementary matrices…
Higher K-theory of toric varieties
Joseph Gubeladze
A natural higher K-theoretic analogue of the triviality of vector bundles on affine toric varieties is the conjecture on nilpotence of the multiplicative action of the natural numb…