Obstructions to weak approximation for reductive groups over p-adic function fields

Yisheng Tian

doi:10.1016/j.jnt.2020.08.008

Obstructions to weak approximation for reductive groups over p-adic function fields

Yisheng Tian

Université Paris-Saclay

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

4 Scopus citations

Abstract

We establish arithmetic duality theorems for short complexes of tori associated to reductive groups over p-adic function fields. Using arithmetic dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split ones) and relate this obstruction to an unramified Galois cohomology group.

Original language	English
Pages (from-to)	128-162
Number of pages	35
Journal	Journal of Number Theory
Volume	220
DOIs	https://doi.org/10.1016/j.jnt.2020.08.008
State	Published - Mar 2021
Externally published	Yes

Keywords

Arithmetic duality theorems
Unramified cohomology
Weak approximation

Access to Document

10.1016/j.jnt.2020.08.008

Cite this

@article{0029f5aec4884b20911311ebaf81f474,

title = "Obstructions to weak approximation for reductive groups over p-adic function fields",

abstract = "We establish arithmetic duality theorems for short complexes of tori associated to reductive groups over p-adic function fields. Using arithmetic dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split ones) and relate this obstruction to an unramified Galois cohomology group.",

keywords = "Arithmetic duality theorems, Unramified cohomology, Weak approximation",

author = "Yisheng Tian",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = mar,

doi = "10.1016/j.jnt.2020.08.008",

language = "英语",

volume = "220",

pages = "128--162",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Obstructions to weak approximation for reductive groups over p-adic function fields

AU - Tian, Yisheng

PY - 2021/3

Y1 - 2021/3

N2 - We establish arithmetic duality theorems for short complexes of tori associated to reductive groups over p-adic function fields. Using arithmetic dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split ones) and relate this obstruction to an unramified Galois cohomology group.

AB - We establish arithmetic duality theorems for short complexes of tori associated to reductive groups over p-adic function fields. Using arithmetic dualities, we deduce obstructions to weak approximation for certain reductive groups (especially quasi-split ones) and relate this obstruction to an unramified Galois cohomology group.

KW - Arithmetic duality theorems

KW - Unramified cohomology

KW - Weak approximation

UR - https://www.scopus.com/pages/publications/85092138216

U2 - 10.1016/j.jnt.2020.08.008

DO - 10.1016/j.jnt.2020.08.008

M3 - 文章

AN - SCOPUS:85092138216

SN - 0022-314X

VL - 220

SP - 128

EP - 162

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Obstructions to weak approximation for reductive groups over p-adic function fields

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this