No CrossRef data available.
Article contents
ON NONCRITICAL GALOIS REPRESENTATIONS
Published online by Cambridge University Press: 22 July 2021
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We propose a conjecture that the Galois representation attached to every Hilbert modular form is noncritical and prove it under certain conditions. Under the same condition we prove Chida, Mok and Park’s conjecture that Fontaine-Mazur L-invariant and Teitelbaum-type L-invariant coincide with each other.
Keywords
MSC classification
Primary:
11F80: Galois representations
- Type
- Research Article
- Information
- Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 1 , January 2023 , pp. 383 - 420
- Copyright
- © The Author(s), 2021. Published by Cambridge University Press
References
Boutot, J.-F. and Carayol, H.,
$p$
-adic uniformization of Shimura curves: the theorems of Cherednik and Drinfeld,
Astérisque
, 196–197 (1991), 45–158.Google Scholar
Carayol, H., On
$\ell$
--adic representations associated with Hilbert modular forms,
Ann. Sci. école Norm. Sup. (4)
, 19 (1986), 409–468.CrossRefGoogle Scholar
Chida, M., Mok, C. and Park, J., On Teitelbaum type
$\mathbf{\mathcal{L}}$
-invariants of Hilbert Modular forms attached to definite quaternions,
J. Number Theory
, 147 (2015), 633–665.CrossRefGoogle Scholar
Coleman, R., Dilogarithms, regulators, and
$p$
-adic
$L$
functions,
Invent. Math.
, 69 (1982), 171–208.CrossRefGoogle Scholar
Coleman, R. and Iovita, A., Hidden structures on Semistable curves,
Astérisque
, 331 (2010), 179–254.Google Scholar
Colmez, P., Extra zeros of
$p$
-adic L-functions of modular forms, in Algebra and Number Theory
(Hindustan Book Agency, Delhi, 2005), pp. 193–210.Google Scholar
Deligne, P., Shimura varieties: modular interpretation and technique of construction of canonical models, Proc. Symp. Pure Math. 33 (2) (1979), 247–290.CrossRefGoogle Scholar
de Sahlit, E., Eichler cohomology and periods of modular froms on
$p$
-adic Schottky groups,
J. Reine Angew. Math.
, 400 (1989) 3–31.Google Scholar
de Shalit, E., Differentials of the second kind on Mumford curves,
Israel J. Math.
, 71 (1990), 1–16.CrossRefGoogle Scholar
Drinfeld, V. G., Coverings of
$p$
-adic symmetric regions,
Funct. Anal. Appl.
, 10 (1976), 107–115.CrossRefGoogle Scholar
Faltings, G., Crystalline cohomology and p-adic Galois-representations, in Algebraic Analysis, Geometry, and Number Theory (Johns Hopkins University Press,
Baltimore, MD, 1989), pp. 25–80.Google Scholar
Faltings, G.,
$F$
-isocrystals on open varieties, results and conjectures, in The Grothendieck Festschrift, Vol. II,
Progr. Math.
, Vol. 87 (Birkhäuser Boston, 1990), pp. 219–248.Google Scholar
Faltings, G., Crystalline cohomology of semistable curve – The
${\mathbb{Q}}_p$
-theory,
J. Algebraic Geom.
, 6 (1997), 1–18.Google Scholar
Greenberg, R. and Stevens, G.,
$p$
-Adic L-functions and
$p$
-adic periods of modular forms,
Invent. Math.
, 111 (1993), 407–447.CrossRefGoogle Scholar
Iovita, A. and Spiess, M., Logarithmic differential forms on
$p$
-adic symmetric spaces,
Duke Math. J.
, 110 (2001), 253–278.CrossRefGoogle Scholar
Iovita, A. and Spiess, M., Derivatives of
$p$
-adic
$L$
-functions, Heegner cycles and monodromy modules attached to modular forms,
Invent. Math.
, 154 (2003), 333–384.CrossRefGoogle Scholar
Mazur, B., Tate, J. and Teitelbaum, J., On
$p$
-adic analogs of the conjectures of Birch and Swinnerton-Dyer,
Invent. Math.
, 84 (1986), 1–48.CrossRefGoogle Scholar
Messing, W.,
The Crystals Associated to Barsotti-Tate Groups: With Applications to Abelian Schemes
, Lecture Notes in Math., Vol. 264, (Springer,
Berlin, 1972).CrossRefGoogle Scholar
Milne, J. S., Canonical models of mixed Shimura varieties and automorphic vector bundles in automorphic forms, in Shimura Varieties and
$L$
-Functions (Academic Press,
New York, 1990), pp. 284–414.Google Scholar
Piatetski-Shapiro, I., Multiplicity one theorems, in Proc. of Symp. in Pure Math., Vol. 33, Part 1 (American Mathematical Society,
Providence, RI, 1979), pp. 209–212.Google Scholar
Rapoport, M. and Zink, T., Period Spaces for
$p$
-Divisible Groups (Princeton University Press,
Princeton, NJ, 1996).Google Scholar
Saito, T., Hilbert modular forms and
$p$
-adic Hodge theory,
Compos. Math.
, 145 (2009), 1081–1113.CrossRefGoogle Scholar
Schneider, P., The cohomology of local systems on
$p$
-adically uniformized varieties,
Math. Ann.
, 293 (1992), 623–650.CrossRefGoogle Scholar
Teitelbaum, J., On Drinfeld’s universal formal group over the
$p$
-adic upper half plane,
Math. Ann.
, 284 (1989), 647–674.CrossRefGoogle Scholar
Teitelbaum, J., Values of
$p$
-adic
$L$
-functions and a
$p$
-adic Poisson kernel,
Invent. Math.
, 101 (1990), 395–410.CrossRefGoogle Scholar
Varshavsky, Y.,
$p$
-Adic uniformization of unitary Shimura varieties,
Publ. Math. IHES
, 87 (1998), 57–119.CrossRefGoogle Scholar
Xie, B., On Drinfeld’s universal special formal module,
J. Number Theory
, 129 (2009), 1122–1135.CrossRefGoogle Scholar
You have
Access