Adjoint L-value formula and Period conjecture

Abstract: For a Hecke eigenform $f$, we state an adjoint L-value formula relative to each division quaternion algebra $D$ over ${\mathbb Q}$ with discriminant $\partial$ and reduced norm $N$. A key to prove the formula is the theta correspondence for the quadratic ${\mathbb Q}$-space $(D,N)$. Under the $R=T$-theorem, the $p$-part of the Bloch-Kato conjecture is known; so, the formula is an adjoint Selmer class number formula. We also describe how to relate the formula to a conjecture on periods of Shimura subvarieties of quaternionic Shimura varieties.

Mathematics

Audience: researchers in the topic

Comments: Zoom number: 743 736 2326

Zoom password: 013049

PKU/BICMR Number Theory Seminar