<div>Let <i>K<sub>0</sub></i>(Var<i><sub>k</sub></i>) be the Grothendieck group of varieties over a field <i>k</i>. We construct an exact category, denoted Add(Var<sub><i>k</i></sub>)<sub><i>S</i></sub>, such that there is a surjection <i>K<sub>0</sub></i>(Var<i>k</i>)→<i>K<sub>0</sub></i>(Add(Var<i><sub>k</sub></i>)<sub><i>S</i></sub>).If we consider only zero dimensional varieties, then this surjection is an isomorphism. Like <i>K<sub>0</sub></i>(Var<i><sub>k</sub></i>), the group K<sub><i>0</i></sub>(Add(Var<sub><i>k</i></sub>)<i><sub>S</sub></i>) is also generated by isomorphism classes of varieties,and we construct motivic measures on <i>K<sub>0</sub></i>(Add(Var<i><sub>k</sub></i>)<i><sub>S</sub></i>) including the Euler characteristic if <i>k</i>=<i>C</i>, and point counting measures and the zeta function if <i>k</i> is finite.<br></div>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/15046497 |
| Date | 23 July 2021 |
| Creators | Harrison Wong (11178198) |
| Source Sets | Purdue University |
| Detected Language | Danish |
| Type | Text, Thesis |
| Rights | CC BY 4.0 |
| Relation | https://figshare.com/articles/thesis/K-theory_of_certain_additive_categories_associated_with_varieties/15046497 |
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