On the Limit of Frobenius in the Grothendieck Group
| Autor: | Kazuhiko Kurano, Kosuke Ohta |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Noetherian
Discrete mathematics Mathematics::Commutative Algebra 13D15 13A35 General Mathematics High Energy Physics::Phenomenology Local ring Mathematics - Commutative Algebra Commutative Algebra (math.AC) FOS: Mathematics Grothendieck group Finitely-generated abelian group Mathematics Fundamental class |
| Zdroj: | Acta Mathematica Vietnamica. 40:161-172 |
| ISSN: | 2315-4144 0251-4184 |
| Popis: | Considering the Grothendieck group modulo numerical equivalence, we obtain the finitely generated lattice $\overline{G_0(R)}$ for a Noetherian local ring $R$. Let $C_{CM}(R)$ be the cone in $\overline{G_0(R)}_{\Bbb R}$ spanned by cycles of maximal Cohen-Macaulay $R$-modules. We shall define the fundamental class $\overline{\mu_R}$ of $R$ in $\overline{G_0(R)}_{\Bbb R}$, which is the limit of the Frobenius direct images (divided by their rank) $[{}^e R]/p^{de}$ in the case ${ch}(R) = p > 0$. The homological conjectures are deeply related to the problems whether $\overline{\mu_R}$ is in the Cohen-Macaulay cone $C_{CM}(R)$ or the strictly nef cone $SN(R)$ defined below. In this paper, we shall prove that $\overline{\mu_R}$ is in $C_{CM}(R)$ in the case where $R$ is FFRT or F-rational. Comment: 13 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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