San Pietro in Montorio
is a late 15th century conventual and titular church on the Gianicolo overlooking Trastevere. The church is dedicated to St Peter the Apostle on the Janiculum, and commands an excellent view of Rome, the valley of the Tiber and its framework of hills.
A medieval tradition claims that this was the site of St Peter's martyrdom, and this is the reason a church dedicated to him was built here. However, there is nothing to support this claim, and it has been established with some certainty that the Apostle was martyred in the Circus of Nero, at the site of San Pietro in Vaticano.
For reference, a plan of the church is available here
The first reference to the church and monastery is from the early 9th century. The monastery become a Benedictine abbey in the 10th century. At the end of the 14th century the monastery passed to the Augustinian Congregation of St Ambrose, also known as Ambrosians or Ambrosiani. After 1438, the church and monastery were abandoned.
In 1472, Pope Sixtus IV handed the disused church and convent over to the reform congregation of the Franciscans, called the Amadeans. In 1481, the friars began to restore the convent, and decided to rebuild the church from its foundations. The new church was initially paid for by funds given by Louis XI, King of France and later by patronage from the King and Queen of Spain, Isabella and Fernando of Castiglia. In 1891 the Reformed friars were absorbed into the Order of Friars Minor (OFM), which continues to have charge of the church.
Photos of the Tempietto here