Geodesic
Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms
Documenta mathematica, Tome 17 (2012), pp. 807-849
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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.
DOI : 10.4171/dm/382
Classification : 11F41, 11F67, 11R23, 14G35
Mots-clés : Iwasawa theory, p-adic L-function, Hilbert modular forms, hida theory, modular symbol 
@article{10_4171_dm_382,
     author = {Tadashi Ochiai},
     title = {Several variables $p$-adic $L$-functions for {Hida} families of {Hilbert} modular forms},
     journal = {Documenta mathematica},
     pages = {807--849},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/382},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/382/}
}
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Tadashi Ochiai. Several variables $p$-adic $L$-functions for Hida families of Hilbert modular forms. Documenta mathematica, Tome 17 (2012), pp. 807-849. doi: 10.4171/dm/382

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