These are the notes for Deligne's seminar, "Periodes des Integrales Abeliennes", I.H.E.S., 1978--79 as written by J.S. Milne. They were published as pp9--100 of Deligne, Pierre; Milne, James S.; Ogus, Arthur; Shih, Kuang-yen. Hodge cycles, motives, and Shimura varieties. Lecture Notes in Mathematics, 900. Springer-Verlag, Berlin-New York, 1982.
1982 Original authentic typed version.
2003 TeXed, corrected, endnotes added. Original numbering retained.
2011 Minor revision. Original numbering retained.
2018 Minor revision. Original numbering retained.

Erratum

The second paragraph in 3.2(a) should read (as in the original): However, the above argument shows the following: let $H^{\prime}$ be the group fixing all tensors occurring in subquotients of $T^{m,n}$s that are fixed by $H$; then $H=H^{\prime}$.

p.26 bottom. As Junecue Sue pointed out to me, $\mathbb{G}_{m}$ should act on $\mathbb{Q}{}(1)$ as $\nu$ not $\nu^{-1}$.