Zobrazeno 1 - 10
of 23
pro vyhledávání: '"Valloni, Domenico"'
Autor:
Valloni, Domenico
In this article, we define supersingular Brauer classes in positive characteristic and study their role in the Brauer-Manin obstruction. We relate this notion to the Brauer group of supersingular K3 surfaces and use our results to study the Brauer-Ma
Externí odkaz:
http://arxiv.org/abs/2412.01785
Autor:
Ambrosi, Emiliano, Valloni, Domenico
Let $k$ be an algebraically closed field of characteristic $p \geq 0$ and $V$ be a faithful $k$-rational representation of a finite $\ell$-group $G$, where $\ell$ is a prime number. The Noether problem asks whether $V/G$ is a stably rational variety.
Externí odkaz:
http://arxiv.org/abs/2302.04153
Autor:
Valloni, Domenico
In this paper, we study maps between moduli spaces of lattice-polarized K3 surfaces induced by sublattices of prime index. We show that these maps can be used to determine if a rational point of the moduli space belongs to the Noether-Lefschetz locus
Externí odkaz:
http://arxiv.org/abs/2210.07375
Autor:
Valloni, Domenico
We use lattice theory to study the isogeny class of a K3 surface. Starting from isotropic Brauer classes, we construct isogenies via Kneser method of neighboring lattices. We also determine the fields of definition of isogenous K3 surfaces, and study
Externí odkaz:
http://arxiv.org/abs/2206.02560
We prove that every element of order 2 in the Brauer group of a complex Kummer surface X descends to an Enriques quotient of X. In 'generic' cases this gives a bijection between the set Enr(X) of Enriques quotients of X up to isomorphism and the set
Externí odkaz:
http://arxiv.org/abs/2202.08030
We study a new object that can be attached to an abelian variety or a complex torus: the invariant Brauer group, as recently defined by Yang Cao. Over the field of complex numbers this is an elementary abelian 2-group with an explicit upper bound on
Externí odkaz:
http://arxiv.org/abs/2007.05473
Autor:
Valloni, Domenico
Let $X/ \mathbb{C}$ be a K3 surface with complex multiplication by the ring of integers of a CM field $E$. We show that $X$ can always be defined over an Abelian extension $K/E$ explicitly determined by the discriminant form of the lattice $\mathrm{N
Externí odkaz:
http://arxiv.org/abs/1907.01336
Autor:
Valloni, Domenico
We study K3 surfaces with complex multiplication following the classical work of Shimura on CM abelian varieties. After we translate the problem in terms of the arithmetic of the CM field and its id\`{e}les, we proceed to study some abelian extension
Externí odkaz:
http://arxiv.org/abs/1804.08763
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