NTS ABSTRACTFall2020: Difference between revisions
(→Sep 3) |
(→Sep 3) |
||
| Line 12: | Line 12: | ||
|- | |- | ||
| bgcolor="#BCD2EE" | | | bgcolor="#BCD2EE" | | ||
In this talk, we study the Chow group of the motive associated to a tempered global L-packet \pi of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of \pi, if the central derivative L'(1/2,\pi) is nonvanishing, then the \pi-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain \pi-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative L'(1/2,\pi) and local doubling zeta integrals. This is a joint work with Chao Li | In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li | ||
|} | |} | ||
</center> | </center> | ||
<br> | <br> | ||
Revision as of 15:56, 26 August 2020
Return to [1]
Sep 3
| Yifeng Liu |
| Beilinson-Bloch conjecture and arithmetic inner product formula |
|
In this talk, we study the Chow group of the motive associated to a tempered global L-packet $\pi$ of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of $\pi$, if the central derivative $L'(1/2,\pi)$ is nonvanishing, then the $\pi$-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson--Bloch conjecture for Chow groups and L-functions. Moreover, assuming the modularity of Kudla's generating functions of special cycles, we explicitly construct elements in a certain $\pi$-nearly isotypic subspace of the Chow group by arithmetic theta lifting, and compute their heights in terms of the central derivative $L'(1/2,\pi)$ and local doubling zeta integrals. This is a joint work with Chao Li |