WEAK APPROXIMATION FOR FANO COMPLETE INTERSECTIONS IN POSITIVE CHARACTERISTIC

Jason M. Starr; Zhiyu Tian; Runhong Zong

doi:10.5802/aif.3495

WEAK APPROXIMATION FOR FANO COMPLETE INTERSECTIONS IN POSITIVE CHARACTERISTIC

Jason M. Starr
, Zhiyu Tian
, Runhong Zong

Mathematics

Peking University
Nanjing University

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

For a smooth curve B over a field k = k with char(k) = p, for every complete intersection X_B in B ×_{Spec k} Pⁿ_k of type (d1, . . ., dc), we prove weak approximation of adelic points of X_B by k(B)-points at all places of (strong) potentially good reduction, if the Fano index is ≥ 2 and if p > max(d1, . . ., dc). This also applies to specializations of complex Fano manifolds with Picard rank 1 and Fano index 1 away from “bad primes”.

Original language	English
Pages (from-to)	1503-1534
Number of pages	32
Journal	Annales de l'Institut Fourier
Volume	72
Issue number	4
DOIs	https://doi.org/10.5802/aif.3495
State	Published - 2022

Keywords

separably rationally connected
stability
weak approximation

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10.5802/aif.3495

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title = "WEAK APPROXIMATION FOR FANO COMPLETE INTERSECTIONS IN POSITIVE CHARACTERISTIC",

abstract = "For a smooth curve B over a field k = k with char(k) = p, for every complete intersection XB in B ×Spec k Pnk of type (d1, . . ., dc), we prove weak approximation of adelic points of XB by k(B)-points at all places of (strong) potentially good reduction, if the Fano index is ≥ 2 and if p > max(d1, . . ., dc). This also applies to specializations of complex Fano manifolds with Picard rank 1 and Fano index 1 away from “bad primes”.",

keywords = "separably rationally connected, stability, weak approximation",

author = "Starr, \{Jason M.\} and Zhiyu Tian and Runhong Zong",

year = "2022",

doi = "10.5802/aif.3495",

language = "English",

volume = "72",

pages = "1503--1534",

journal = "Annales de l'Institut Fourier",

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TY - JOUR

T1 - WEAK APPROXIMATION FOR FANO COMPLETE INTERSECTIONS IN POSITIVE CHARACTERISTIC

AU - Starr, Jason M.

AU - Tian, Zhiyu

AU - Zong, Runhong

PY - 2022

Y1 - 2022

N2 - For a smooth curve B over a field k = k with char(k) = p, for every complete intersection XB in B ×Spec k Pnk of type (d1, . . ., dc), we prove weak approximation of adelic points of XB by k(B)-points at all places of (strong) potentially good reduction, if the Fano index is ≥ 2 and if p > max(d1, . . ., dc). This also applies to specializations of complex Fano manifolds with Picard rank 1 and Fano index 1 away from “bad primes”.

AB - For a smooth curve B over a field k = k with char(k) = p, for every complete intersection XB in B ×Spec k Pnk of type (d1, . . ., dc), we prove weak approximation of adelic points of XB by k(B)-points at all places of (strong) potentially good reduction, if the Fano index is ≥ 2 and if p > max(d1, . . ., dc). This also applies to specializations of complex Fano manifolds with Picard rank 1 and Fano index 1 away from “bad primes”.

KW - separably rationally connected

KW - stability

KW - weak approximation

UR - https://www.scopus.com/pages/publications/85141871828

U2 - 10.5802/aif.3495

DO - 10.5802/aif.3495

M3 - Article

AN - SCOPUS:85141871828

SN - 0373-0956

VL - 72

SP - 1503

EP - 1534

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 4

ER -

WEAK APPROXIMATION FOR FANO COMPLETE INTERSECTIONS IN POSITIVE CHARACTERISTIC

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Keywords

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