arXiv:1102.2273 Degrees of periods from arXiv Front: math.NT by Jianming Wan We introduce the concept of degree to classify the periods in the sense of Kontsevich. Using this notion we give some new understanding of some problems in transcendental number theory.
http://ncatlab.org/nlab/show/period
http://mathoverflow.net/questions/99791/on-grothendiecks-period-relations
nLab page on Periods