School of Mathematics Seminars and Lectures

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

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

Wednesday, November 23, 2022 from to (Asia/Kolkata)
at 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.