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pro vyhledávání: '"11G10"'
We first give a cleaner and more direct approach to the derivation of the Fast model of the Kummer surface. We show how to construct efficient (N,N)-isogenies, for any odd N, both on the general Kummer surface and on the Fast model.
Comment: 38
Comment: 38
Externí odkaz:
http://arxiv.org/abs/2409.14819
We give a categorical description of all abelian varieties with commutative endomorphism ring over a finite field with $q=p^a$ elements in a fixed isogeny class in terms of pairs consisting of a fractional $\mathbb Z[\pi,q/\pi]$-ideal and a fractiona
Externí odkaz:
http://arxiv.org/abs/2409.08865
Autor:
Gonzalez-Hernandez, Alvaro
We study the birational geometry of the Kummer surfaces associated to the Jacobian varieties of genus two curves, with a particular focus on fields of characteristic two. In order to do so, we explicitly compute a projective embedding of the Jacobian
Externí odkaz:
http://arxiv.org/abs/2409.04532
Autor:
Moakher, Mohamed
We generalize a result of Ribet and Takahashi on the parametrization of elliptic curves by Shimura curves to the Hilbert modular setting. In particular, we study the behaviour of the parametrization of modular abelian varieties by Shimura curves asso
Externí odkaz:
http://arxiv.org/abs/2408.15410
We prove that the dual fine Selmer group of an abelian variety over the unramified $\mathbb{Z}_{p}$-extension of a function field is finitely generated over $\mathbb{Z}_{p}$. This is a function field version of a conjecture of Coates--Sujatha. We fur
Externí odkaz:
http://arxiv.org/abs/2408.06938
Autor:
Kunzweiler, Sabrina, Robert, Damien
We present an unconditional CRT algorithm to compute the modular polynomial $\Phi_\ell(X,Y)$ in quasi-linear time. The main ingredients of our algorithm are: the embedding of $\ell$-isogenies in smooth-degree isogenies in higher dimension, and the co
Externí odkaz:
http://arxiv.org/abs/2408.06990
In this manuscript we consider a special complex torus, denoted $S_{\Delta_{2k}}$ (for each $k \in \mathbb{N},\, k \geq 1$) and called the Dirac spinor torus. It is an Abelian variety of complex dimension $2^{k}$ whose covering space is the space of
Externí odkaz:
http://arxiv.org/abs/2408.05511
We characterise abelian surfaces defined over finite fields containing no curves of genus less than or equal to $3$. Firstly, we complete and expand the characterisation of isogeny classes of abelian surfaces with no curves of genus up to $2$ initiat
Externí odkaz:
http://arxiv.org/abs/2408.02493
We give several formulas for how Iwasawa $\mu$-invariants of abelian varieties over unramified $\mathbb{Z}_{p}$-extensions of function fields change under isogeny. These are analogues of Schneider's formula in the number field setting. We also prove
Externí odkaz:
http://arxiv.org/abs/2407.21431
Autor:
Ramakrishnan, Dinakar
Let E be an elliptic curve over a number field F, A the abelian surface E x E, and T_F(A) the F-rational albanese kernel of A, which is a subgroup of the degree zero part of Chow group of zero cycles on A modulo rational equivalence. The first result
Externí odkaz:
http://arxiv.org/abs/2407.20468