descent / relegation / decline
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descent
The movement from a higher point to a lower point; going down or descending.
Der Abstieg vom Gipfel war wegen des losen Gerölls sehr gefährlich.
The descent from the summit was very dangerous because of the loose scree.
'Der Abstieg' is the noun formed from the separable verb 'absteigen' (to descend / get off). The verb is made up of 'ab' (down) and 'steigen' (to go, climb). So the noun always describes a movement or development downward.
Nach dem langen Aufstieg war der Abstieg eine Erleichterung.
After the long ascent, the descent was a relief.
In its literal meaning, 'Abstieg' is often combined with places one descends from. Typical phrases are 'der Abstieg vom Berg' (the descent from the mountain) or 'der Abstieg ins Tal' (the descent into the valley).
Der Abstieg vom Gipfel dauerte zwei Stunden.
The descent from the summit took two hours.
In a sports context, especially in football/soccer, 'der Abstieg' almost always means relegation, that is, dropping into a lower league. Fixed expressions include 'gegen den Abstieg kämpfen' (to fight against relegation) and 'den Abstieg verhindern' (to prevent relegation).
Die Mannschaft kämpft in dieser Saison gegen den Abstieg.
The team is fighting against relegation this season.
When it is about society or the economy, 'Abstieg' describes a loss of status or prosperity. People often speak of 'sozialer Abstieg' (social decline) or 'wirtschaftlicher Abstieg' (economic decline).
Viele Menschen haben Angst vor dem sozialen Abstieg.
Many people are afraid of social decline.
ascent / rise
'der Aufstieg' and 'der Abstieg' are opposites. 'Aufstieg' means movement upward or an improvement in position, for example in a career or in sports. 'Abstieg' means movement downward or a loss of position, reputation, or quality. When hiking, it is about the direction on the mountain. In sports, it is about whether a team moves into a higher or lower league. In short: 'Aufstieg' goes up, 'Abstieg' goes down.
Nach einer schwachen Saison konnte das Team den Abstieg nicht mehr verhindern.
After a weak season, the team could no longer prevent relegation.
Nach dem letzten Sieg feierte der Verein den Aufstieg in die zweite Liga.
After the final victory, the club celebrated promotion to the second division.