I took this picture a few days ago in Val Rendena, in the dolomitic Brenta group (2000 m). The whole plant was 15 cm tall at most, and it had a single leaf on the stem. What flower is it?
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I had a look at white-flowered plants flowering in July in a site about the flora of the French Alps, and the best I could find was Parnassia palustris: http://www.florealpes.com/fiche_parnassie.php
At this developmental stage, it looks quite similar to your photo, with the same kind of structures at the base of the petals. The site says that there are heart-shaped leaves at the base, plus one on the stem. This last leaf matches your description. The site says it can grow up to 2500m.
The Italian Wikipedia says:
In Italia è presente solo nelle regioni settentrionali e centrali, nonché in Campania. In montagna si spinge fino a circa 2000 m, ma sulle Alpi è stata segnalata anche a quote superiori (3000 m sul versante svizzero del Monte Rosa).
This means that it can be found in the Italian Alps too, including at 2000m.