Zobrazeno 1 - 10
of 39
pro vyhledávání: '"SPRINGER, CALEB"'
In this paper, we study questions of definability and decidability for infinite algebraic extensions ${\bf K}$ of $\mathbb{F}_p(t)$ and their subrings of $\mathcal{S}$-integral functions. We focus on fields ${\bf K}$ satisfying a local property which
Externí odkaz:
http://arxiv.org/abs/2411.14960
Publikováno v:
The Bulletin of Symbolic Logic, 2023 Dec 01. 29(4), 626-655.
Externí odkaz:
https://www.jstor.org/stable/27285435
Autor:
Marseglia, Stefano, Springer, Caleb
We study the groups of rational points of abelian varieties defined over a finite field $ \mathbb{F}_q$ whose endomorphism rings are commutative, or, equivalently, whose isogeny classes are determined by squarefree characteristic polynomials. When $\
Externí odkaz:
http://arxiv.org/abs/2211.15280
Autor:
Springer, Caleb
We show that the ring of integers of $\mathbb{Q}^{\text{tr}}$ is existentially definable in the ring of integers of $\mathbb{Q}^{\text{tr}}(i)$, where $\mathbb{Q}^{\text{tr}}$ denotes the field of all totally real numbers. This implies that the ring
Externí odkaz:
http://arxiv.org/abs/2207.00140
Autor:
Marseglia, Stefano, Springer, Caleb
We show that every finite abelian group $G$ occurs as the group of rational points of an ordinary abelian variety over $\mathbb{F}_2$, $\mathbb{F}_3$ and $\mathbb{F}_5$. We produce partial results for abelian varieties over a general finite field $\m
Externí odkaz:
http://arxiv.org/abs/2105.08125
Autor:
Arul, Vishal, Booher, Jeremy, Groen, Steven R., Howe, Everett W., Li, Wanlin, Matei, Vlad, Pries, Rachel, Springer, Caleb
We study the extent to which curves over finite fields are characterized by their zeta functions and the zeta functions of certain of their covers. Suppose C and C' are curves over a finite field K, with K-rational base points P and P', and let D and
Externí odkaz:
http://arxiv.org/abs/2102.11419
For any subset $Z \subseteq \mathbb{Q}$, consider the set $S_Z$ of subfields $L\subseteq \overline{\mathbb{Q}}$ which contain a co-infinite subset $C \subseteq L$ that is universally definable in $L$ such that $C \cap \mathbb{Q}=Z$. Placing a natural
Externí odkaz:
http://arxiv.org/abs/2010.09551
Autor:
Springer, Caleb
Publikováno v:
European Journal of Mathematics (2021)
Let $A$ be a simple abelian variety of dimension $g$ defined over a finite field $\mathbb{F}_q$ with Frobenius endomorphism $\pi$. This paper describes the structure of the group of rational points $A(\mathbb{F}_{q^n})$, for all $n \geq 1$, as a modu
Externí odkaz:
http://arxiv.org/abs/2006.00637
Autor:
Costa, Edgar, Donepudi, Ravi, Fernando, Ravi, Karemaker, Valentijn, Springer, Caleb, West, Mckenzie
Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that
Externí odkaz:
http://arxiv.org/abs/2002.02067
Autor:
Springer, Caleb
We produce new examples of totally imaginary infinite extensions of $\mathbb{Q}$ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for $\mathbb{Q}^{(2)}$. In particular, we use parametri
Externí odkaz:
http://arxiv.org/abs/1910.01239