Motives and Siegel modular forms (Q2772973)

Given a motive \(M\) over \(\mathbb Q\), by using invariant theory the author defines the fundamental periods of \(M\), which generalize Deligne's periods. If \(M\) is constructed from \(n\) motives \(M_1, \ldots, M_n\) by a standard algebraic operation, he shows that the fundamental periods of \(M\) can be expressed as monomials of the fundamental periods of \(M_1, \ldots, M_n\). As an application, he also discusses two motives attached to a Siegel modular form and proves that a Siegel modular form of degree \(m\) has at most \(m+1\) period invariants.