Die Polizei verhaftet den Täter am Tatort.

Polizei is a feminine noun in German, so in the nominative singular it takes die: die Polizei.

A useful thing to know is that die Polizei is grammatically singular, even though in English the police often behaves like a plural idea. So German says:

• Die Polizei verhaftet den Täter. = The police arrest/is arresting the perpetrator.

If you want to talk about individual police officers instead, you would use a different noun, such as:

• die Polizisten = the police officers

So die Polizei means the police as an institution or force.

Because den Täter is the direct object of the sentence, so it must be in the accusative case.

The verb verhaften means to arrest. The one doing the action is the subject:

• die Polizei = the police

The one receiving the action is the direct object:

• den Täter = the perpetrator / offender

Since Täter is a masculine noun, its article changes like this:

• nominative: der Täter
• accusative: den Täter

So:

• Der Täter = the perpetrator (as subject)
• Die Polizei verhaftet den Täter. = the police arrest the perpetrator (object)

In German, case endings often tell you this.

In your sentence:

• die Polizei is nominative, so it is the subject
• den Täter is accusative, so it is the direct object

That means:

• die Polizei = the one doing the arresting
• den Täter = the one being arrested

This is one reason German can sometimes change word order more freely than English. Even if you moved things around, the case marking still helps show who is doing what.

Am Tatort means at the crime scene.

Grammatically, am is a contraction of:

• an dem → am

So:

• an dem Tatort becomes am Tatort

This is very common in German:

• am Bahnhof = at the station
• am Montag = on Monday
• am Tatort = at the crime scene

Here, Tatort is in the dative case because it follows the preposition an in a location sense.

German uses different prepositions depending on how a place is viewed.

• an often suggests being at a place, sometimes more as a point or location
• in suggests being in(side) something

A Tatort is usually thought of as a location where a crime happened, so German normally says:

• am Tatort = at the crime scene

Using im Tatort would sound unnatural in normal German.

So this is something you should mostly learn as a fixed expression:

• am Tatort

Because German main clauses usually follow the verb-second rule (V2).

In a normal statement, the finite verb comes second:

• Die Polizei | verhaftet | den Täter am Tatort.

The first position is taken by Die Polizei, and the verb comes right after it.

German does not mean the second word literally; it means the second sentence element. For example:

• Am Tatort verhaftet die Polizei den Täter.

Here, Am Tatort is the first element, and verhaftet is still second.

Yes, verhaftet is present tense: the 3rd person singular form of verhaften.

• ich verhafte
• du verhaftest
• er/sie/es verhaftet

German present tense can often correspond to either English:

• arrests
• is arresting

The exact translation depends on context. Without more context, Die Polizei verhaftet den Täter am Tatort could mean either:

• The police arrest the perpetrator at the crime scene
• The police are arresting the perpetrator at the crime scene

German often uses the simple present where English might prefer the progressive.

This is a difference between the two languages.

In English, the police is a plural-looking expression and often takes a plural verb:

• The police are arresting him.

In German, die Polizei is a singular feminine noun, so it takes a singular verb:

• Die Polizei verhaftet ihn.

So even though the meaning may involve multiple officers, the grammar is singular.

If you want an explicitly plural noun in German, you could say:

• Die Polizisten verhaften den Täter. = The police officers arrest the perpetrator.

The base form is der Täter.

It usually means:

• perpetrator
• offender
• sometimes culprit, depending on context

It comes from the verb tun / the noun idea of doing an act, and it refers to a person who commits an offense or crime.

Its forms are:

• nominative: der Täter
• accusative: den Täter
• dative: dem Täter
• genitive: des Täters

Plural:

• die Täter

Yes. German word order is more flexible than English, as long as the verb stays in second position in a main clause and the case marking still makes the roles clear.

For example:

• Die Polizei verhaftet den Täter am Tatort.
• Am Tatort verhaftet die Polizei den Täter.

Both are correct. The second version emphasizes the location more.

You could also hear:

• Den Täter verhaftet die Polizei am Tatort.

This is grammatically possible, but it sounds more marked or emphatic because the object is placed first.

So the original sentence is the most neutral order, but other orders are possible for emphasis.

It actually does — it is just hidden inside am.

• am = an dem

So:

• am Tatort literally contains dem

That means the article is there, just contracted.

You will see this a lot in German:

• am = an dem
• im = in dem
• vom = von dem
• zum = zu dem

So am Tatort is not missing an article; it is simply using the normal contracted form.

Yes. That is also a very natural sentence.

• Die Polizei verhaftet den Täter am Tatort. = present tense
• Die Polizei hat den Täter am Tatort verhaftet. = perfect tense

The second one usually means:

• The police have arrested / arrested the perpetrator at the crime scene

In everyday spoken German, the perfect tense (hat ... verhaftet) is very common for past events. The present-tense version is still correct, but it describes a present-time action or can be used in certain narrative styles.