# Search results

Journal of Number Theory > 2015 > 147 > Complete > 156-171

Mathematische Nachrichten > 295 > 5 > 890 - 911

*K*be a finitely generated extension of its prime field and let $e\ge 2$ be an integer. We prove the injectivity part of the section conjecture of Grothendieck for almost all $\sigma :=({\sigma}_{1},\text{\u2026},{\sigma}_{e})\in \mathrm{Gal}{\left(K\right)}^{e}$ and for all smooth geometrically integral projective curves of genus ≥1 over the field $\stackrel{\sim}{K}\left(\sigma \right)$.

Mathematische Nachrichten > 293 > 11 > 2175 - 2186

Research in Number Theory > 2019 > 5 > 4 > 1-17

*A*isogenous to $$B^r$$ Br , where the characteristic polynomial

*g*of Frobenius of

*B*is an ordinary square-free

*q*-Weil polynomial, for a power

*q*of a prime

*p*, or a square-free

*p*-Weil polynomial with no real roots. Under some extra assumptions on the polynomial

*g*we give an explicit description of all...

Fundamenta Informaticae > 2019 > Vol. 169, nr 4 > 275--283

_{n}* (in particular the group order of ℤ*

_{n}). It is also known that factorization of square-free integer n can be reduced to the problem of computing the group order of an elliptic curve E/ℤ

_{n}. In this paper we describe the analogous reduction for computing...

Mathematische Nachrichten > 292 > 8 > 1716 - 1726

*A*with good ordinary reduction over a finite extension of ${Q}_{p}$ with

*p*an odd prime, the Albanese kernel of

*A*is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety

*G*over a perfect field

*k*, we construct a decreasing integral filtration ${\left\{{F}^{r}\right\}}_{r\ge 0}$ of...

ANNALI DELL'UNIVERSITA' DI FERRARA > 2019 > 65 > 1 > 127-137

*S*should behave when pulled-back to the self-product $$S^m$$ S m for $$m>p_g(S)$$ m > p g ( S ) . We show that Voisin’s conjecture is true for a 3-dimensional family of surfaces of general type with $$p_g=q=2$$ p g = q = 2 and $$K^2=7$$ K 2 = 7 constructed by Cancian and Frapporti, and revisited...

Mathematische Nachrichten > 291 > 17-18 > 2599 - 2630

Journal of Number Theory > 2018 > 193 > C > 213-234

Mathematische Zeitschrift > 2019 > 292 > 1-2 > 655-675

Journal of Algebra > 2018 > 510 > C > 393-412

Advances in Mathematics > 2018 > 335 > C > 896-909

Journal of Number Theory > 2018 > 183 > C > 352-387

Selecta Mathematica > 2018 > 24 > 1 > 63-84

Advances in Mathematics > 2017 > 318 > C > 459-496

The Ramanujan Journal > 2018 > 46 > 1 > 201-227

*K*3 surfaces parametrized by Klein’s icosahedral invariants. Via the periods and the Shioda–Inose structures of

*K*3 surfaces, the special values of icosahedral invariants generate class fields over quartic CM fields. Moreover, we give an explicit expression of the canonical...

Research in Number Theory > 2017 > 3 > 1 > 1-12

*g*, let $$\mathrm {Sp}_{2g}(R)$$ Sp 2 g ( R ) denote the group of $$2g \times 2g$$ 2 g × 2 g symplectic matrices over a ring

*R*. Assume $$g \ge 2$$ g ≥ 2 . For a prime number $$\ell $$ ℓ , we give a self-contained proof that any closed subgroup of $$\mathrm {Sp}_{2g}(\mathbb {Z}_\ell )$$ Sp 2 g ( Z ℓ ) which surjects...

European Journal of Mathematics > 2017 > 3 > 3 > 507-519

*k*. We also compute the Grothendieck group of the category of

*A*-isotypic abelian varieties, for any simple abelian variety

*A*, assuming

*k*has characteristic 0, and for any elliptic curve

*A*in any characteristic.