Semantic Scholar Open Access 2014 3 sitasi

An Analytic Description of Local Intersection Numbers at Non-Archimedian Places for Products of Semi-Stable Curves

J. Kolb

Lihat Sumber DOI

Abstrak

We generalise a formula of Shou-Wu Zhang, which describes local arithmetic intersection numbers of three Cartier divisors with support in the special fibre on a a self-product of a semi-stable arithmetic surface using elementary analysis. By an approximation argument, Zhang extends his formula to a formula for local arithmetic intersection numbers of three adelic metrized line bundles on the self-product of a curve with trivial underlying line bundle. Using the results on intersection theory from arXiv:1404.1623 [math.AG] we generalize these results to d-fold self-products for arbitrary d. For the approximations to converge, we have to assume that d satisfies the vanishing condition 4.7 from arXiv:1404.1623 [math.AG], which is true at least for $d\in \{2,3,4,5\}$.

Topik & Kata Kunci

Mathematics

Penulis (1)

J. Kolb

Format Sitasi

APA MLA BibTeX

Kolb, J. (2014). An Analytic Description of Local Intersection Numbers at Non-Archimedian Places for Products of Semi-Stable Curves. https://doi.org/10.5802/AFST.1486

Akses Cepat

Lihat di Sumber doi.org/10.5802/AFST.1486

Informasi Jurnal

Tahun Terbit: 2014
Bahasa: en
Total Sitasi: 3×
Sumber Database: Semantic Scholar
DOI: 10.5802/AFST.1486
Akses: Open Access ✓