Speaker: Haruzo Hida
Affiliation: University of California, USA
Title: Adjoint $L$-value formula and Tate conjecture
Date and Time: May 31, 2023, 15:00:00 Hours
Venue: AG-77
Asbtract: For a Hecke eigenform $f$, we state an adjoint $L$-value formula relative to each quaternion algebra $D$ over ${\mathbf Q}$ with discriminant $\partial$ and reduced norm $N$. A key to prove the formula is the theta correspondence for the quadratic ${\mathbf Q}$-space $(D,N)$. Under the $R=T$-theorem, $p$-part of the Bloch-Kato conjecture is known; so, the formula is an adjoint Selmer class number formula. We also sketch how to prove by the formula a consequence of the Tate conjecture for quaternionic Shimura varieties.
Affiliation: University of California, USA
Title: Adjoint $L$-value formula and Tate conjecture
Date and Time: May 31, 2023, 15:00:00 Hours
Venue: AG-77
Asbtract: For a Hecke eigenform $f$, we state an adjoint $L$-value formula relative to each quaternion algebra $D$ over ${\mathbf Q}$ with discriminant $\partial$ and reduced norm $N$. A key to prove the formula is the theta correspondence for the quadratic ${\mathbf Q}$-space $(D,N)$. Under the $R=T$-theorem, $p$-part of the Bloch-Kato conjecture is known; so, the formula is an adjoint Selmer class number formula. We also sketch how to prove by the formula a consequence of the Tate conjecture for quaternionic Shimura varieties.