Question: Where is the monument built by the Emperor Trajan in the style of the influential Nile-based civilization located?

Context paragraphs:
Temple of Trajan: The Temple of Trajan was a Roman temple dedicated to the emperor Trajan and his wife Plotina after his deification by the Roman Senate.  It was built in the Forum of Trajan (Rome), by Trajan's adoptive son and successor Hadrian, between 125 and 138.  It was destroyed in the Middle Ages.

Ancient Egyptian architecture: Ancient Egyptian architecture is the architecture of Ancient Egypt, one of the most influential civilizations throughout history, which developed a vast array of diverse structures and great architectural monuments along the Nile, including pyramids and temples.

Trajan's Kiosk: Trajan's Kiosk is a hypaethral temple located on Agilkia Island.  One of the largest Ancient Egyptian monuments standing today, it was constructed by the Roman Emperor, Trajan.  The edifice was originally built on the island of Philae, near the lower Aswan Dam.  However, it was later transported to Agilika in the 1960s by UNESCO to save it from being enveloped by the rising waters of the Nile due to the construction of the Aswan High Dam.

Basilica Ulpia: The Basilica Ulpia was an ancient Roman civic building located in the Forum of Trajan.  The Basilica Ulpia separates the temple from the main courtyard in the Forum of Trajan with the Trajan's Column to the northwest.  It was named after Roman emperor Trajan whose full name was Marcus Ulpius Traianus.

Trajan's Column: Trajan's Column (Italian: "Colonna Traiana" , Latin: "COLVMNA·TRAIANI" ) is a Roman triumphal column in Rome, Italy, that commemorates Roman emperor Trajan's victory in the Dacian Wars.  It was probably constructed under the supervision of the architect Apollodorus of Damascus at the order of the Roman Senate.  It is located in Trajan's Forum, built near the Quirinal Hill, north of the Roman Forum.  Completed in AD 113, the freestanding column is most famous for its spiral bas relief, which artistically describes the epic wars between the Romans and Dacians (101–102 and 105–106).  Its design has inspired numerous victory columns, both ancient and modern.

Ludus Magnus: The Ludus Magnus or The Great Gladiatorial Training School is the largest of the gladiatorial arenas in Rome, Italy.  It was built by the emperor Domitian (81-96 AD) in the valley between the Esquiline and the Caelian hills, an area already occupied by Republican and Augustan structures.  The still visible ruins of the monument belong to a second building stage attributed to the emperor Trajan (98-117), where the Ludus plane was raised by about 1.5 m .

Ulpian Library: The Bibliotheca Ulpia ("Ulpian Library") was a Roman library founded by the Emperor Trajan in AD 114 in his forum, the Forum of Trajan, located in ancient Rome.  was considered one of the most prominent and most famous libraries of antiquity, (the Library of Alexandria of the ancient city of Rome).  Indeed, it was considered the major library in the Western World upon the destruction of the Library of Alexandria in the 3rd century.  “Venantius Fortunatus also writes of ‘Vergil recited in Trajan's forum in the city’ about 576 AD.”  It was the only Roman library to survive until the Fall of Rome in the mid-fifth century.

Tropaeum Traiani: The Tropaeum Traiani is a monument in Roman Civitas Tropaensium (site of modern Adamclisi, Romania), built in 109 in then Moesia Inferior, to commemorate Roman Emperor Trajan's victory over the Dacians, in the winter of 101-102, in the Battle of Adamclisi.  Before Trajan's construction, an altar existed there, on the walls of which were inscribed the names of the 3,000 legionaries and auxilia (servicemen) who had died "fighting for the Republic".  (Latin: Tropaeum from Greek: Tropaion, source of English: "trophy").

Arch of Trajan (Ancona): The Arch of Trajan in Ancona is a Roman Triumphal arch erected by the Senate and people of Rome in the reign of Emperor Trajan.  It was built in honour of that Emperor after he expanded the port of the city out of his own pocket, improving the docks and the fortifications.  It was from here that Trajan departed for the ultimately successful war against the Dacians, an episode which is commemorated in the bas relief of Trajan's column in Rome.

Statue of Trajan, Tower Hill: The statue of Trajan is an outdoor late-eighteenth-century bronze sculpture depicting Roman Emperor Trajan, located in front of a section of the London Wall built by Romans, at Tower Hill in London, United Kingdom.  He is shown bareheaded and wearing a tunic, holding a scroll in his left hand while gesturing with his right hand raised.  A plaque at its base contains the inscription: There is no information presented at the site about the sculptor or date.

Supporting paragraphs: Trajan's Kiosk Ancient Egyptian architecture
Answer: Agilkia Island