Anual Mensual Semanal Hoy Buscar Ir al mes específico Enero Febrero Marzo Abril Mayo Junio Julio Agosto Septiembre Octubre Noviembre Diciembre 2019 2020 2021 2022 2023 2024 2025 2026
seminarios Teoría de Números

seminarios Teoría de Números

Numerical equivalence of $mathbb R$-divisors and Shioda-Tate formula for arithmetic varieties

SPEAKER: Paolo Dolce (University of Udine)

DATE & TIME: Tuesday, March 02nd, 2021 - 17:30

ABSTRACT: Let $X$ be an arithmetic variety over the ring of integers of a number field $K$, and let $X_K$ be its generic fiber. 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 Néron-Severi group of $X_K$. This is a higher dimensional and arithmetic version of the classical Shioda-Tate
formula for elliptic surfaces. Such analogy is strengthened by the fact that we also show that the numerically trivial arithmetic $mathbb R$-divisors on $X$ are exactly the linear combinations of principal ones.

como siempre a través de Teams

Localización DATE & TIME: Tuesday, March 02nd, 2021 - 17:30