Arithmetic Theta Kernel and Liftings
Shimura Varieties and LFunctions March 13, 2023  March 17, 2023
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Kudla program
arithmetic SiegelWeil formulas
modularity
Arithmetic Theta Kernel And Liftings
Let $K=\Q(\sqrt d)$ be an imaginary quadratic field. Let $L$ be a unimodular $O_K$lattice of signature $(n1, 1)$, and let $\mathcal X$ be the compactified Shimura variety over $O_K$ associated at $L$. In this talk, we describe roughly how to construct an arithmetic theta series (arithmetic theta kernel), and prove that it is a modular form of level $d$, weight $n$, character $\chi_d^n$ with values in $\widehat{CH}^1(\mathcal X^*)$. Using this arithmetic theta kernel, we can produce classical modular forms from arithmetic $1$cycles (Faltings’ height pairing) and produce arithmetic divisors from classical cusp forms. This is joint work with Bruinier, Howard, Kudla, and Rapoport for $n \ge 3$. The case $2$ is a joint work in progress with Qiao He and Yousheng Shi.
Arithmetic Theta Kernel and Liftings

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Arithmetic Theta Kernel And Liftings
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