Dolce, Paolo and Gualdi, Roberto (2022) Numerical equivalence of R-divisors and Shioda-Tate formula for arithmetic varieties. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2022 (784). pp. 131-154. ISSN 0075-4102, 1435-5345
Full text not available from this repository. (Request a copy)Abstract
Let X be an arithmetic variety over the ring of integers of a number field K, with smooth generic fiber X-K. We give a formula that relates the dimension of the first Arakelov-Chow vector space of X with the Mordell-Weil rank of the Albanese variety of X-K and the rank of the Neron-Seven group of X-K. This is a higher-dimensional and arithmetic version of the classical Shioda-Tate formula for elliptic surfaces. Such an analogy is strengthened by the fact that we show that the numerically trivial arithmetic R-divisors on X are exactly the linear combinations of principal ones. This result is equivalent to the non-degeneracy of the arithmetic intersection pairing in the argument of divisors, partially confirming a conjecture by H. Gillet and C. Soule.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | HODGE INDEX THEOREM; ABELIAN-VARIETIES; BUNDLES |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Feb 2024 07:53 |
| Last Modified: | 08 Feb 2024 07:53 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57403 |
Actions (login required)
 |
View Item |
