Several-variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations
J Tilouine, E Urban - Annales Scientifiques de l'École Normale Supérieure, 1999 - Elsevier
Let F be a totally real field and G= GSp (4)/F. In this paper, we show under a weak
assumption that, given a Hecke eigensystem λ which is (p, P)-ordinary for a fixed parabolic P …
assumption that, given a Hecke eigensystem λ which is (p, P)-ordinary for a fixed parabolic P …
Euler systems for GSp (4)
D Loeffler, C Skinner, SL Zerbes - arXiv preprint arXiv:1706.00201, 2017 - arxiv.org
arXiv:1706.00201v4 [math.NT] 26 Jan 2021 Page 1 EULER SYSTEMS FOR GSP(4) DAVID
LOEFFLER, CHRISTOPHER SKINNER, AND SARAH LIVIA ZERBES Abstract. We construct an …
LOEFFLER, CHRISTOPHER SKINNER, AND SARAH LIVIA ZERBES Abstract. We construct an …
Nearly ordinary Galois deformations over arbitrary number fields
F Calegari, B Mazur - Journal of the Institute of Mathematics of …, 2009 - cambridge.org
Let K be an arbitrary number field, and let ρ: Gal (/K)→ GL2 (E) be a nearly ordinary
irreducible geometric Galois representation. In this paper, we study the nearly ordinary …
irreducible geometric Galois representation. In this paper, we study the nearly ordinary …
Higher coherent cohomology and -adic modular forms of singular weights
V Pilloni - 2020 - projecteuclid.org
Higher coherent cohomology andp-adic modular forms of singular weights Page 1 HIGHER
COHERENT COHOMOLOGY AND p-ADIC MODULAR FORMS OF SINGULAR WEIGHTS V …
COHERENT COHOMOLOGY AND p-ADIC MODULAR FORMS OF SINGULAR WEIGHTS V …
Sur les déformations p-adiques de certaines représentations automorphes
C Skinner, E Urban - Journal of the Institute of Mathematics of …, 2006 - cambridge.org
Résumé Par une méthode entierement nouvelle utilisant les déformations p-adiques de
pentes positives de représentations automorphes pour GSp4/Q, nous prouvons que le p …
pentes positives de représentations automorphes pour GSp4/Q, nous prouvons que le p …
Cohomology of Siegel varieties with p-adic integral coefficients and applications
A Mokrane, J Tilouine - arXiv preprint math/0012090, 2000 - arxiv.org
Under the assumption that Galois representations associated to Siegel modular forms exist
(it is known only for genus at most 2), we show that the cohomology with p-adic integral …
(it is known only for genus at most 2), we show that the cohomology with p-adic integral …
Galois representations for general symplectic groups
A Kret, SW Shin - arXiv preprint arXiv:1609.04223, 2016 - arxiv.org
We prove the existence of GSpin-valued Galois representations corresponding to
cohomological cuspidal automorphic representations of general symplectic groups over …
cohomological cuspidal automorphic representations of general symplectic groups over …
On the Bloch-Kato conjecture for GSp (4)
D Loeffler, SL Zerbes - arXiv preprint arXiv:2003.05960, 2020 - arxiv.org
We prove an explicit reciprocity law for the Euler system attached to the spin motive of a
genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa …
genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa …
Saito–Kurokawa lifts and applications to the Bloch–Kato conjecture
J Brown - Compositio Mathematica, 2007 - cambridge.org
Let f be a newform of weight 2k− 2 and level 1. In this paper we provide evidence for the
Bloch–Kato conjecture for modular forms. We demonstrate an implication that under suitable …
Bloch–Kato conjecture for modular forms. We demonstrate an implication that under suitable …
On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
D Loeffler, SL Zerbes - arXiv preprint arXiv:2110.13102, 2021 - arxiv.org
Let $ A $ be a modular abelian surface over $ Q $ which either has trivial geometric
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …
endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an …