On fields with Serre's property (F) and the finitude of Galois and flat cohomology of algebraic groups over fields

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Title:	On fields with Serre's property (F) and the finitude of Galois and flat cohomology of algebraic groups over fields
Authors:	ID Duy Tân, Nguyêñ (Author) ID Quôc Thǎńg, Nguyêñ (Author)
Files:	AMC_Duy_Tân,_Quôc_Thǎńg_2026.pdf (559,47 KB) MD5: 50CE2D7D3BE64B5596FE3F3A747F84C1
Language:	English
Work type:	Article
Typology:	1.01 - Original Scientific Article
Organization:	ZUP - University of Primorska Press
Abstract:	In this paper, we revisit and strengthen the property (F) introduced by Serre for perfect fields and relate it with some some general conditions guaranteeing the finiteness (and also the infinitude) of Galois cohomology of unipotent algebraic groups over fields of positive characteristic and consider some examples.
Keywords:	Unipotent group, Galois cohomology
Publication status:	Published
Publication version:	Version of Record
Publication date:	04.06.2026
Publisher:	Založba Univerze na Primorskem
Year of publishing:	2026
Number of pages:	29 str.
Numbering:	Vol. 26, no. 3, [article no.] P3.04
PID:	20.500.12556/RUP-23507
UDC:	51
eISSN:	1855-3974
DOI:	10.26493/1855-3974.3639.1f7
Publication date in RUP:	17.08.2026
Views:	25
Downloads:	1
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Title:	Ars mathematica contemporanea
Publisher:	Založba Univerze na Primorskem
ISSN:	1855-3974

Funder:	VAST
Project number:	NVCC01.01/2025-2025

License:	CC BY 4.0, Creative Commons Attribution 4.0 International

Link:	http://creativecommons.org/licenses/by/4.0/
Description:	This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Language:	Slovenian
Title:	O poljih s Serrovo lastnostjo (F) ter o končnosti Galoisove in ploske kohomologije algebraičnih grup nad polji
Abstract:	V tem članku ponovno obravnavamo in okrepimo lastnost (F ), ki jo je za popolna polja uvedel Serre, ter jo povežemo z nekaterimi splošnimi pogoji, ki zagotavljajo končnost (pa tudi neskončnost) Galoisove kohomologije unipotentnih algebraičnih grup nad polji pozitivne karakteristike. Obravnavamo tudi več ilustrativnih primerov.
Keywords:	Unipotentna grupa, Galoisova kohomologija

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