K-theoretic balancing conditions and the Grothendieck group of a toric variety

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10452301" target="_blank" >RIV/00216208:11320/22:10452301 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wjozV2qKMZ" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=wjozV2qKMZ</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jalgebra.2022.07.038" target="_blank" >10.1016/j.jalgebra.2022.07.038</a>

Result language
angličtina
Original language name
K-theoretic balancing conditions and the Grothendieck group of a toric variety
Original language description
We introduce a ring of Z-valued functions on a complete fan Δcalled Grothendieck weights to describe the ordinary operational K-theory of the associated toric variety X. These functions satisfy a K-theoretic analogue of the balancing condition for Minkowski weights, which is induced by a presentation of the Grothendieck group of X. We explicitly give a combinatorial presentation in low dimensions, and relate Grothendieck weights to other fan-based invariants such as piecewise exponential functions and Minkowski weights. As an application, we give an example of a projective toric surface Xsuch that the forgetful map K°T(X) RIGHTWARDS ARROWK°(X)is not surjective.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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