Geodesic
Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
Documenta mathematica, Tome 17 (2012), pp. 807-849.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: After formulating Conjecture A for $p$-adic $L$-functions defined over ordinary Hilbert modular Hida deformations on a totally real field $F$ of degree $d$, we construct two $p$-adic $L$-functions of $d+1$-variable depending on the parity of weight as a partial result on Conjecture A. We will also state Conjecture B which is a corollary of Conjecture A but is important by itself. Main issues of the construction are the study of Hida theory of Hilbert modular forms by using Hilbert modular varieties (without using Shimura curves), the study of higher dimensional modular symbols on Hilbert modular varieties and delicate treatments on archimedean and $p$-adic periods.
Classification : 11R23, 11F41, 14G35, 11F67
Keywords: $p$-adic $L$-function, Hilbert modular forms, hida theory, Iwasawa theory, modular symbol 
@article{DOCMA_2012__17__a6,
     author = {Ochiai, Tadashi},
     title = {Several variables $p$-adic $L$-functions for {Hida} families of {Hilbert} modular forms},
     journal = {Documenta mathematica},
     pages = {807--849},
     publisher = {mathdoc},
     volume = {17},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a6/}
}
TY  - JOUR
AU  - Ochiai, Tadashi
TI  - Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
JO  - Documenta mathematica
PY  - 2012
SP  - 807
EP  - 849
VL  - 17
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a6/
LA  - en
ID  - DOCMA_2012__17__a6
ER  - 
%0 Journal Article
%A Ochiai, Tadashi
%T Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
%J Documenta mathematica
%D 2012
%P 807-849
%V 17
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a6/
%G en
%F DOCMA_2012__17__a6
Ochiai, Tadashi. Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms. Documenta mathematica, Tome 17 (2012), pp. 807-849. http://geodesic.mathdoc.fr/item/DOCMA_2012__17__a6/