On a conjecture of Xiao.
On a Convolution of L-Series.
On a covering group theorem and its applications.
On a family of elliptic curves.
On a family of elliptic curves of rank at least 2
Let be a family of elliptic curves over , where is a positive integer and , are distinct odd primes. We study the torsion part and the rank of . More specifically, we prove that the torsion subgroup of is trivial and the -rank of this family is at least 2, whenever , and with neither nor dividing .
On a Fermat Equation Arising in the Arithmetic Theory of Function Fields.
On a formula of Beniamino Segre.
On a Galois extension with restricted ramification related to the Selmer group of an elliptic curve with complex multiplication.
On a general difference Galois theory I
We know well difference Picard-Vessiot theory, Galois theory of linear difference equations. We propose a general Galois theory of difference equations that generalizes Picard-Vessiot theory. For every difference field extension of characteristic , we attach its Galois group, which is a group of coordinate transformation.
On a general difference Galois theory II
We apply the General Galois Theory of difference equations introduced in the first part to concrete examples. The General Galois Theory allows us to define a discrete dynamical system being infinitesimally solvable, which is a finer notion than being integrable. We determine all the infinitesimally solvable discrete dynamical systems on the compact Riemann surfaces.
On a generalization of Hilbert's 21st problem
On a generalization of Tate dualities with application to Iwasawa theory
On a Geometric Interpretation of Multiplicity.
On a geometric property of the normal bundle of surfaces in IP4.
On a Grauert-Riemenschneider vanishing theorem for Frobenius split varieties in characteristic p.
On a lifting problem for principal Dedekind domains
On a linearity criterion for algebraic systems of divisors on a projective variety
In the present paper, it is established in any characteristic the validity of a classical theorem of Enriques', stating the linearity of any algebraic system of divisors on a projective variety, which has index 1 and whose generic element is irreducible, as soon as its dimension is at least 2.
On a local property of good frames in Thom-Boardman singularities
On a noncommutative Iwasawa main conjecture for varieties over finite fields
We formulate and prove an analogue of the noncommutative Iwasawa main conjecture for -adic Lie extensions of a separated scheme of finite type over a finite field of characteristic prime to .
On a problem concerning quasianalytic local rings
Let (ₙ)ₙ be a quasianalytic differentiable system. Let m ∈ ℕ. We consider the following problem: let and f̂ be its Taylor series at . Split the set of exponents into two disjoint subsets A and B, , and decompose the formal series f̂ into the sum of two formal series G and H, supported by A and B, respectively. Do there exist with Taylor series at zero G and H, respectively? The main result of this paper is the following: if we have a positive answer to the above problem for some m ≥ 2, then...