Difference between revisions of "NTS ABSTRACTFall2020"
(Created page with "Return to [https://www.math.wisc.edu/wiki/index.php/NTS ] == Sep 3 == <center> {| style="color:black; font-size:100%" table border="2" cellpadding="10" width="700" cellspac...") |
(→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 | |
|} | |} | ||
</center> | </center> | ||
<br> | <br> |
Revision as of 10:55, 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 |