Adjoint L-value formula and its relation to the Tate conjecture.

by Prof. Haruzo Hida (University of California at Los Angeles)

Wednesday 23 Nov 2022, 14:00 → 15:00 Asia/Kolkata

AG-77

Abstract: For a Hecke eigenform $f$, we state an adjoint L-value formula relative to each 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 $R={\mathbb T}$-theorem, $p$-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 consequence of the Tate conjecture for quaternionic Shimura varieties.