Galois action on universal covers of Kodaira fibrations

2020 ◽  
Vol 169 (7) ◽  
pp. 1281-1303
Author(s):  
Gabino González-Diez
2001 ◽  
Vol 353 (9) ◽  
pp. 3585-3602 ◽  
Author(s):  
Christina Sormani ◽  
Guofang Wei

2001 ◽  
Vol 12 (08) ◽  
pp. 943-972 ◽  
Author(s):  
CATERINA CONSANI ◽  
JASPER SCHOLTEN

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.


2021 ◽  
Vol 92 ◽  
pp. 101686
Author(s):  
Ji-won Park ◽  
Otfried Cheong
Keyword(s):  

2020 ◽  
Vol 14 (7) ◽  
pp. 1953-1979
Author(s):  
Noelia Rizo ◽  
A. A. Schaeffer Fry ◽  
Carolina Vallejo

Author(s):  
DANIEL J. WOODHOUSE

Abstract Leighton’s graph covering theorem states that a pair of finite graphs with isomorphic universal covers have a common finite cover. We provide a new proof of Leighton’s theorem that allows generalisations; we prove the corresponding result for graphs with fins. As a corollary we obtain pattern rigidity for free groups with line patterns, building on the work of Cashen–Macura and Hagen–Touikan. To illustrate the potential for future applications, we give a quasi-isometric rigidity result for a family of cyclic doubles of free groups.


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