On l-independence of algebraic monodromy groups in compatible systems of representations.
On Manin's conjecture for a certain singular cubic surface
On modular representations of Gal (.../Q) arising from modular forms.
On non-basic Rapoport-Zink spaces
In this paper we study certain moduli spaces of Barsotti-Tate groups constructed by Rapoport and Zink as local analogues of Shimura varieties. More precisely, given an isogeny class of Barsotti-Tate groups with unramified additional structures, we investigate how the associated (non-basic) moduli spaces compare to the (basic) moduli spaces associated with its isoclinic constituents. This aspect of the geometry of the Rapoport-Zink spaces is closely related to Kottwitz’s prediction that their -adic...
On octahedral extensions of and quadratic -curves
We give a necessary condition for a surjective representation Gal to arise from the -torsion of a -curve. We pay a special attention to the case of quadratic -curves.
On -adic -functions
On p-adic analogues of the conjectures of Birch and Swinnerton-Dyer.
On periods and quasi-periods of Drinfeld modules
On power values of pyramidal numbers, I
On ramification and genus of recursive towers.
On ranks of Jacobian varieties in prime degree extensions
T. Dokchitser [Acta Arith. 126 (2007)] showed that given an elliptic curve E defined over a number field K then there are infinitely many degree 3 extensions L/K for which the rank of E(L) is larger than E(K). In the present paper we show that the same is true if we replace 3 by any prime number. This result follows from a more general result establishing a similar property for the Jacobian varieties associated with curves defined by an equation of the shape f(y) = g(x) where f and g are polynomials...
On rational torsion points of central -curves
Let be a central -curve over a polyquadratic field . In this article we give an upper bound for prime divisors of the order of the -rational torsion subgroup (see Theorems 1.1 and 1.2). The notion of central -curves is a generalization of that of elliptic curves over . Our result is a generalization of Theorem 2 of Mazur [12], and it is a precision of the upper bounds of Merel [15] and Oesterlé [17].
On Schertz's class number formula related to elliptic units for some non-Galois extensions
On second 2-descent and non-congruent numbers
We use the so-called second 2-descent method to find several series of non-congruent numbers. We consider three different 2-isogenies of the congruent elliptic curves and their duals, and find a necessary condition to estimate the size of the images of the 2-Selmer groups in the Selmer groups of the isogeny.
On Siegel modular forms. Part I.
On simultaneous arithmetic progressions on elliptic curves.
On singular and supersingular invariants of Drinfeld modules
On singular moduli for rank 2 Drinfeld modules
On some characteristic polynomials attached to finite Drinfeld modules.
On some elliptic curves with large sha.