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제목 [정수론] The motivic nature of the discrete Hodge star operator
발표자 김도형 ( University of Michigan ) 날짜 2018-06-08
Host KAIST Place (E6-1) Room 4415
Abstract The conjecture of Prasanna-Venkatesh predicts that the rational cohomology ring of an arithmetic manifold has special endomorphisms of a motivic origin. Their motivic nature allows one to test the conjecture indirectly through various regulator maps, but the source of these endomorphisms remains mysterious. We propose that the discrete Hodge star operator supplies the predicted endomorphisms in the case when the arithmetic manifold in question is uniformized by the upper half-space. In order to justify the proposal, we analyze how two different rational structures in cohomology interact with the discrete and geometric Hodge star operators, and show that the difference between them is measured by a special value of an L-function. Numerical examples will be given to illustrate the result.

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