author={Caterina Consani and Jasper L. J. Scholten},
  journal={International Journal of Mathematics},
This paper investigates some aspects of the arithmetic of a quintic threefold in Pr4 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 , whose associated (continuous system of) Galois representation(s) appears to be the most likely candidate to induce… 
Since the 90s, we know that all elliptic curves defined over Q are modular, and the (almost proven) Serre conjectures imply that the same is true more generally for every odd 2-dimensional Galois
Exponential sums, hypersurfaces with many symmetries and Galois representations
The main theme of this thesis is the study of compatible systems of `-adic Galois representations provided by the étale cohomology of arithmetic varieties with a large group of symmetries. A
Sato-Tate groups of some weight 3 motives
We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h 3,0 = h 2,1 = h 1,2 = h 0,3 = 1. We then describe
Hilbert modularity of some double octic Calabi–Yau threefolds
Quaternionic Manin symbols, Brandt matrices, and Hilbert modular forms
A more efficient way to compute Hilbert modular forms over totally real number fields, especially quadratic fields, and a theory of quaternionic M-symbols whose definition bears some resemblance to the classical M-Symbols, except for their combinatorial nature is developed.
Superspecial abelian varieties, theta series and the Jacquet-Langlands correspondence
2.1. Section 1.4. Traverso’s Boundedness Conjecture. p.34-36. It is best to simply ignore Section 1.4 and Subsection 1.5.1., as they are not used in the rest of the thesis. For readers interested in
We prove that the Consani-Scholten quintic, a Calabi-Yau three- fold over Q, is Hilbert modular. For this, we refine several techniques known from the context of modular forms. Most notably, we


Cycles, L-functions and triple products of elliptic curves.
A variant of a conjecture of Beilinson and Bloch relates the rank of the Griffiths group of a smooth projective variety over a number field to the order of vanishing of an L-function at the center of
On Zeta Functions of Quaternion Algebras
The present paper is concerned with some equalities between zeta functions of quaternion algebras introduced in Godement [6], Shimura [11], Tamagawa [13]. Let A be a quaternion algebra over a totally
On the modularity of elliptic curves over Q
In this paper, building on work of Wiles [Wi] and of Wiles and one of us (R.T.) [TW], we will prove the following two theorems (see §2.2). Theorem A. If E/Q is an elliptic curve, then E is modular.
The quaternionic bridge between elliptic curves and Hilbert modular forms
The main result of this thesis is a matching between an elliptic curve E over F = Q(√509) which has good reduction everywhere, and a normalized holomorphic Hilbert modular eigenform f for F of
Automorphic forms on Adele groups
This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of
On automorphisms of quaternion orders.
Bass Orders play a very important role in different contexts. They were introduced by M. Eichler in [5] under the name of primitive Orders in division quaternion algebras over the rational numbers: A
Traces of Eichler—Brandt matrices and type numbers of quaternion orders
LetA be a totally definite quaternion algebra over a totally real algebraic number fieldF andM be the ring of algebraic integers ofF. For anyM-orderG ofA we derive formulas for the massm(G) and the
On embedding numbers into quaternion orders
A generalization of the chevalley-Hasse-Noether theorem from maximal orders to arbitrary Eichler orders in quaternion algebras is given. A stability property for the numbers of orbits for unit groups
Ring-Theoretic Properties of Certain Hecke Algebras
The purpose of this article is to provide a key ingredient of [W2] by establishing that certain minimal Hecke algebras considered there are complete intersections. As is recorded in [W2], a method
Orders in quaternion algebras.
On etudie certains ordres dans des algebres de quaternions et on developpe une formule de trace calculable pour les matrices de Brandt associees a ces ordres speciaux