Homology, Homotopy and Applications

Volume 1 (1999)

Number 1

$K$-theory of affine toric varieties

Pages: 135 – 145

DOI: http://dx.doi.org/10.4310/HHA.1999.v1.n1.a5

Author

Joseph Gubeladze (A. Razmadze Mathematical Institute, Georgian Academy of Sciences, Tbilisi, Republic of Georgia)

Abstract

This is an updated and expanded version of my preprint #68 in the $K$-theory server at Urbana (which was an abstract of my talk at Vechta conference on commutative algebra, 1994.) In section 2, two conjectures on nilpontency of the ‘monoid Frobenius action’ on the $K$-theory of toric cones and on stabilizations of the corresponding $K$-groups are stated. Both of these conjectures are higher analogues of Anderson’s conjecture and their proof would bring a rather complete understanding of $K$-theory of toric varieties/semigroup rings.

Keywords

toric varieties, projective modules, algebraic $K$-theory, monoid rings

2010 Mathematics Subject Classification

Primary 19-02. Secondary 14M25.

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