
verweisen auf
to refer to
To point something out or direct attention to something; to refer to something.
Der Autor verweist in der Fußnote auf eine weiterführende Studie.
The author refers in the footnote to a further study.
to refer / expel
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to refer to
To point something out or direct attention to something; to refer to something.
Der Autor verweist in der Fußnote auf eine weiterführende Studie.
The author refers in the footnote to a further study.

to expel someone
To officially exclude or send someone away from an institution (e.g., school) or a place (e.g., country, hall).
Nach wiederholtem Stören des Unterrichts wurde der Schüler der Schule verwiesen.
After repeatedly disrupting the lesson, the student was expelled from the school.

to refer someone
To send someone on to another person or responsible office for information or help.
Die Sekretärin konnte mir nicht helfen und verwies mich an die Personalabteilung.
The secretary could not help me and referred me to the HR department.

to relegate someone
In a sports competition, to be better than a competitor and thus place them in a lower rank.
Der Läufer aus Kenia verwies seine Gegner souverän auf die Plätze.
The runner from Kenya confidently relegated his opponents to the lower places.
'Verweisen' (to refer/expel) is an inseparable verb based on the basic verb 'weisen' (to point/show). The prefix 'ver-' directs the action of pointing toward something else or away from a place.
Der Professor verwies auf die Wichtigkeit der Quellenangaben.
The professor referred to the importance of citing sources.
When pointing to a source, a piece of information, or a connection, the fixed structure is always 'verweisen auf' + accusative. This phrase is typical of academic and formal texts.
Für weitere Details verweise ich auf das Handbuch.
For further details, I refer you to the manual.
To exclude someone from a place, there are two constructions. The very formal variant uses the genitive: 'jemanden des Landes verweisen' (to expel someone from the country). More common is the variant with 'aus' + dative: 'jemanden aus dem Raum verweisen' (to expel someone from the room).
Der Spieler wurde nach der roten Karte des Feldes verwiesen.
The player was sent off the field after the red card.
When sending a person to another place for help or information, you use the structure 'jemanden an' + accusative. The person being sent away is also in the accusative.
Der Arzt verwies mich an einen Spezialisten.
The doctor referred me to a specialist.
The phrase 'jemanden auf die Plätze verweisen' (to relegate someone to the lower places) is a fixed idiom and is used almost exclusively in sports reporting. It means that an athlete was better than their competitors.
Die Schwimmerin verwies ihre Konkurrenz auf die Plätze zwei und drei.
The swimmer relegated her competition to second and third place.
to refer / move into / receive
Sich beziehen auf mainly describes a connection in terms of content. Verweisen auf deliberately directs attention to a specific passage or source so that further information can be found there. Use beziehen for a simple relationship and verweisen for deliberately directing someone to another source.

Dieser Absatz verweist für die genaue Definition auf das erste Kapitel.
For the precise definition, this paragraph refers to the first chapter.
Dieser Absatz bezieht sich inhaltlich auf die Definition im ersten Kapitel.
This paragraph is related in content to the definition in the first chapter.