Introduction to the monodromy conjecture
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917605678252032 |
|---|---|
| author | Veys, Willem |
| author_facet | Veys, Willem |
| contents | The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the $p$-adic Igusa zeta function of $f$ should induce monodromy eigenvalues of $f$. The case of interest is when the zero set of $f$ has singular points. We first present some history and motivation. Then we expose a proof in the case of two variables, and partial results in higher dimension, together with geometric theorems of independent interest inspired by the conjecture. We conclude with several possible generalizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03343 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Introduction to the monodromy conjecture Veys, Willem Algebraic Geometry Number Theory The monodromy conjecture is a mysterious open problem in singularity theory. Its original version relates arithmetic and topological/geometric properties of a multivariate polynomial $f$ over the integers, more precisely, poles of the $p$-adic Igusa zeta function of $f$ should induce monodromy eigenvalues of $f$. The case of interest is when the zero set of $f$ has singular points. We first present some history and motivation. Then we expose a proof in the case of two variables, and partial results in higher dimension, together with geometric theorems of independent interest inspired by the conjecture. We conclude with several possible generalizations. |
| title | Introduction to the monodromy conjecture |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2403.03343 |