scholarly journals On Galois Representations via Siegel Modular Forms of Genus Two

2001 ◽  
Vol 8 (4) ◽  
pp. 577-588 ◽  
Author(s):  
Michael Dettweiler ◽  
Ulf Kühn ◽  
Stefan Reiter
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Siegel Modular Forms ◽  
Genus Two

scholarly journals Computations of Siegel modular forms of genus two

1992 ◽  
Vol 58 (197) ◽  
pp. 381-381 ◽  
Author(s):  
Nils-Peter Skoruppa
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two

On the Graded Ring of Siegel Modular Forms of Genus Two

1965 ◽  
Vol 87 (2) ◽  
pp. 502 ◽  
Author(s):  
William F. Hammond
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Graded Ring ◽  
Genus Two

scholarly journals Level stripping for Siegel modular forms with reducible Galois representations

2013 ◽  
Vol 133 (5) ◽  
pp. 1492-1501
Author(s):  
Jim Brown ◽  
Rodney Keaton
Keyword(s):  
Modular Forms ◽  
Galois Representations ◽  
Siegel Modular Forms

scholarly journals Covariants of binary sextics and vector-valued Siegel modular forms of genus two

2017 ◽  
Vol 369 (3-4) ◽  
pp. 1649-1669 ◽  
Author(s):  
Fabien Cléry ◽  
Carel Faber ◽  
Gerard van der Geer
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two ◽  
Vector Valued

On Siegel Modular Forms of Genus Two

1962 ◽  
Vol 84 (1) ◽  
pp. 175 ◽  
Author(s):  
Jun-Ichi Igusa
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two

On Siegel Modular Forms of Genus Two (II)

1964 ◽  
Vol 86 (2) ◽  
pp. 392 ◽  
Author(s):  
Jun-Ichi Igusa
Keyword(s):  
Modular Forms ◽  
Siegel Modular Forms ◽  
Genus Two

scholarly journals Irreducibility of limits of Galois representations of Saito–Kurokawa type

2021 ◽  
Vol 7 (3) ◽  
Author(s):  
Tobias Berger ◽  
Krzysztof Klosin
Keyword(s):  
Modular Form ◽  
Modular Forms ◽  
Galois Representations ◽  
Siegel Modular Forms ◽  
Selmer Groups ◽  
Two Dimensional ◽  
Elliptic Modular Form

AbstractWe prove (under certain assumptions) the irreducibility of the limit $$\sigma _2$$ σ 2 of a sequence of irreducible essentially self-dual Galois representations $$\sigma _k: G_{{\mathbf {Q}}} \rightarrow {{\,\mathrm{GL}\,}}_4(\overline{{\mathbf {Q}}}_p)$$ σ k : G Q → GL 4 ( Q ¯ p ) (as k approaches 2 in a p-adic sense) which mod p reduce (after semi-simplifying) to $$1 \oplus \rho \oplus \chi $$ 1 ⊕ ρ ⊕ χ with $$\rho $$ ρ irreducible, two-dimensional of determinant $$\chi $$ χ , where $$\chi $$ χ is the mod p cyclotomic character. More precisely, we assume that $$\sigma _k$$ σ k are crystalline (with a particular choice of weights) and Siegel-ordinary at p. Such representations arise in the study of p-adic families of Siegel modular forms and properties of their limits as $$k\rightarrow 2$$ k → 2 appear to be important in the context of the Paramodular Conjecture. The result is deduced from the finiteness of two Selmer groups whose order is controlled by p-adic L-values of an elliptic modular form (giving rise to $$\rho $$ ρ ) which we assume are non-zero.

Sign in / Sign up

Export Citation Format

Share Document