The Grothendieck ring of varieties and of the theory of algebraically closed fields
| Autor: | Tibor Beke |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Pure mathematics Ring (mathematics) Algebra and Number Theory Sieve (category theory) 010102 general mathematics 01 natural sciences Kernel (algebra) Mathematics::Algebraic Geometry Grothendieck topology Mathematics::K-Theory and Homology Mathematics::Category Theory Homotopy hypothesis 0103 physical sciences Grothendieck group Homomorphism 010307 mathematical physics 0101 mathematics Subfunctor Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 221:393-400 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2016.06.014 |
| Popis: | In each characteristic, there is a canonical homomorphism from the Grothendieck ring of varieties to the Grothendieck ring of sets definable in the theory of algebraically closed fields. We prove that this homomorphism is an isomorphism in characteristic zero. In positive characteristics, we exhibit specific elements in the kernel of the corresponding homomorphism of Grothendieck semirings. The comparison of these two Grothendieck rings in positive characteristics seems to be an open question, related to the difficult problem of cancellativity of the Grothendieck semigroup of varieties. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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