Learn Russian: Кто-то принёс цветы погибшему герою. - Someone brought flowers to the fallen hero.

It is formed from the perfective verb погибнуть (to perish/die). To form the active past participle, we look at the masculine past tense form: погиб. Because this stem ends in a consonant (б), we add the suffix -ш- instead of -вш-, creating the base form погибший (the one who perished / the fallen).

Why does the participle end in -ему here?

Participles decline exactly like adjectives, meaning they must agree with the noun they describe in gender, number, and case. The flowers were brought to the hero, which requires the dative case (герою). Therefore, the participle takes the masculine dative ending -ему, becoming погибшему.

Why does this sentence use погибшему instead of the participle for the regular verb "to die" (умершему)?

Погибнуть specifically implies a sudden, tragic, or violent death, such as dying in battle, a disaster, or an accident. It is the direct equivalent of "to fall in combat" or "to perish." Using the standard verb for dying (умереть) wouldn't convey the same honorable or tragic nuance expected when talking about a hero.

Could I use кто-нибудь instead of кто-то to say "someone" here?