scholarly journals The Galois action on geometric lattices and the mod- $$\ell $$ ℓ I/OM

2018 ◽  
Vol 213 (2) ◽  
pp. 371-459 ◽  
Author(s):  
Adam Topaz
Keyword(s):  
Galois Action ◽  
Geometric Lattices

ARITHMETIC ON A QUINTIC THREEFOLD

2001 ◽  
Vol 12 (08) ◽  
pp. 943-972 ◽  
Author(s):  
CATERINA CONSANI ◽  
JASPER SCHOLTEN
Keyword(s):  
Modular Form ◽  
Theta Series ◽  
Continuous System ◽  
Galois Representation ◽  
Hilbert Modular Form ◽  
Galois Action ◽  
Hilbert Modular ◽  
Common Eigenvector ◽  
Quintic Threefold ◽  
Real Quadratic

This paper investigates some aspects of the arithmetic of a quintic threefold in Pr 4 with double points singularities. Particular emphasis is given to the study of the L-function of the Galois action ρ on the middle ℓ-adic cohomology. The main result of the paper is the proof of the existence of a Hilbert modular form of weight (2, 4) and conductor 30, on the real quadratic field [Formula: see text], whose associated (continuous system of) Galois representation(s) appears to be the most likely candidate to induce the scalar extension [Formula: see text]. The Hilbert modular form is interpreted as a common eigenvector of the Brandt matrices which describe the action of the Hecke operators on a space of theta series associated to the norm form of a quaternion algebra over [Formula: see text] and a related Eichler order.

scholarly journals Galois action on the principal block and cyclic Sylow subgroups

2020 ◽  
Vol 14 (7) ◽  
pp. 1953-1979
Author(s):  
Noelia Rizo ◽  
A. A. Schaeffer Fry ◽  
Carolina Vallejo
Keyword(s):  
Sylow Subgroups ◽  
Principal Block ◽  
Galois Action

scholarly journals A class of geometric lattices

1960 ◽  
Vol 66 (2) ◽  
pp. 118-124 ◽  
Author(s):  
K. Rogers ◽  
E. G. Straus
Keyword(s):  
Geometric Lattices
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