Algebraic K -theory and Grothendieck–Witt theory of monoid schemes
| Autor: | Jens Niklas Eberhardt, Oliver Lorscheid, Matthew B. Young |
|---|---|
| Přispěvatelé: | Dynamical Systems, Geometry & Mathematical Physics |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Projective bundle formula
Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Algebraic K-theory Grothendieck–Witt theory General Mathematics Mathematics::Category Theory Mathematics - K-Theory and Homology FOS: Mathematics K-Theory and Homology (math.KT) 19D10 Algebraic Geometry (math.AG) Monoid schemes |
| Zdroj: | Mathematische zeitschrift, 301(2), 1407-1445 Mathematische Zeitschrift |
| ISSN: | 0025-5874 |
| DOI: | 10.1007/s00209-021-02919-z |
| Popis: | We study the algebraic $$K\!$$ K -theory and Grothendieck–Witt theory of proto-exact categories of vector bundles over monoid schemes. Our main results are the complete description of the algebraic $$K\!$$ K -theory space of an integral monoid scheme X in terms of its Picard group $${{\,\mathrm{Pic}\,}}(X)$$ Pic ( X ) and pointed monoid of regular functions $$\Gamma (X, {\mathcal {O}}_X)$$ Γ ( X , O X ) and a complete description of the Grothendieck–Witt space of X in terms of an additional involution on $${{\,\mathrm{Pic}\,}}(X)$$ Pic ( X ) . We also prove space-level projective bundle formulae in both settings. |
| Databáze: | OpenAIRE |
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