arXiv 1608.076432016-08math.NT

An automorphic variant of the Deligne conjecture

Jie Lin

备注：: To appear in Contemporary Mathematics. Some typos corrected. The title is slightly changed due to personal preference. arXiv admin note: text overlap with arXiv:1511.03519

英文摘要：

In this paper we introduce an automorphic variant of the Deligne conjecture for tensor product of two motives over a quadratic imaginary field. On one hand, we define some motivic periods and rewrite the Deligne conjecture in terms of these periods. On the other hand, we define the automorphic analogue of these motivic periods and then give a purely automorphic variant of the Deligne conjecture. At last, we introduce some known results of this automorphic variant.

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