Irrationality of motivic zeta functions
| Autor: | Michael Larsen, Valery A. Lunts |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Class (set theory) 11F80 14G10 General Mathematics 14G10 (Primary) 11F80 14F42 14K15 (Secondary) Rational function K3 surfaces 01 natural sciences Motivic zeta function K3 surface Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry 0103 physical sciences FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Mathematics 14F42 Ring (mathematics) Conjecture motivic zeta functions Galois representations 010102 general mathematics Galois module 14K15 010307 mathematical physics Element (category theory) |
| Zdroj: | Duke Math. J. 169, no. 1 (2020), 1-30 |
| ISSN: | 0012-7094 |
| DOI: | 10.1215/00127094-2019-0035 |
| Popis: | Let $K_0(\mathrm{Var}_{\mathbb{Q}})[1/\mathbb{L}]$ denote the Grothendieck ring of $\mathbb{Q}$-varieties with the Lefschetz class inverted. We show that there exists a K3 surface X over $\mathbb{Q}$ such that the motivic zeta function $\zeta_X(t) := \sum_n [\mathrm{Sym}^n X]t^n$ regarded as an element in $K_0(\mathrm{Var}_{\mathbb{Q}})[1/\mathbb{L}][[t]]$ is not a rational function in $t$, thus disproving a conjecture of Denef and Loeser. Comment: 25 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|