On the p-adic Beilinson conjecture for number fields

p-adic Beilinson conjecture for ordinary Hecke motives associated to imaginary quadratic fields

Factorization of p-adic Rankin L-series

We prove that the p-adic L-series of the tensor square of a p-ordinary modular form factors as the product of the symmetric square p-adic L-series of the form and a Kubota– Leopoldt p-adic L-series. This establishes a generalization of a conjecture of Citro. Greenberg’s exceptional zero conjecture for the adjoint follows as a corollary of our theorem. Our method of proof follows that of Gross, ...

p-ADIC ELLIPTIC POLYLOGARITHM, p-ADIC EISENSTEIN SERIES AND KATZ MEASURE By KENICHI BANNAI and GUIDO KINGS

The specializations of the motivic elliptic polylogarithm on the universal elliptic curve to the modular curve are referred to as Eisenstein classes. In this paper, we prove that the syntomic realization of the Eisenstein classes restricted to the ordinary locus of the modular curve may be expressed using p-adic Eisenstein series of negative weight, which are p-adic modular forms defined using ...

Behavior of $R$-groups for $p$-adic inner forms of quasi-split special unitary groups

‎We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups‎. ‎We prove Arthur's conjecture‎, ‎the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group‎, ‎for quasi-split special unitary groups and their inner forms‎. ‎Furthermore‎, ‎we investigate the invariance of the Knapp-Stein $R$-group within $L$-packets and between inner forms‎. ‎This w...

WEAK BLOCH-BEILINSON CONJECTURE FOR ZERO-CYCLES OVER p-ADIC FIELDS

Contents Introduction 2 1. Homology theory, cycle map, and Kato complex 6 2. Vanishing theorem 10 3. Bertini theorem over a discrete valuation ring 14 4. Surjectivity of cycle map 17 5. Blowup formula and moving lemma 19 6. Proof of main theorem 21 7. Applications of main theorem 23 References 25 1 2 SHUJI SAITO AND KANETOMO SATO