Zobrazeno 1 - 10
of 269
pro vyhledávání: '"12H10"'
Autor:
Ino, Kai, Sanchez, Omar Leon
We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic $p$ equipped
Externí odkaz:
http://arxiv.org/abs/2410.17892
Autor:
Paré, Robert
Partial difference operators for a large class of functors between presheaf categories are introduced, extending our difference operator from \cite{Par24} to the multivariable case. These combine into the Jacobian profunctor which provides the settin
Externí odkaz:
http://arxiv.org/abs/2409.09494
We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a difference va
Externí odkaz:
http://arxiv.org/abs/2406.00880
Autor:
Kamensky, Moshe, Moosa, Rahim
A binding group theorem is proved in the context of quantifier-free internality to the fixed field in difference-closed fields of characteristic zero. This is articulated as a statement about the birational geometry of isotrivial algebraic dynamical
Externí odkaz:
http://arxiv.org/abs/2405.06092
It was recently conjectured that every component of a discrete-time rational dynamical system is a solution to an algebraic difference equation that is linear in its highest-shift term (a quasi-linear equation). We prove that the conjecture holds in
Externí odkaz:
http://arxiv.org/abs/2404.19136
Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version of higher
Externí odkaz:
http://arxiv.org/abs/2403.18170
We classify order $3$ linear difference operators over $\mathbb{C}(x)$ that are solvable in terms of lower order difference operators. To prove this result, we introduce the notion of absolute irreducibility for difference modules, and classify modul
Externí odkaz:
http://arxiv.org/abs/2402.03868
Autor:
Gan, Aiping, Guo, Li
Publikováno v:
Journal of Algebra and its Applications (2023): 2550012
A differential operator of weight $\lambda$ is the algebraic abstraction of the difference quotient $d_\lambda(f)(x):=\big(f(x+\lambda)-f(x)\big)/\lambda$, including both the derivation as $\lambda$ approaches to $0$ and the difference operator when
Externí odkaz:
http://arxiv.org/abs/2402.02282
Autor:
Du, Lixin
We extend the criterion on the existence of telescopers for hypergeometric terms to the case of P-recursive sequences. This criterion is based on the concept of integral bases and the generalized Abramov-Petkovsek reduction for P-recursive sequences.
Externí odkaz:
http://arxiv.org/abs/2311.06065
Autor:
Houédry, Pierre
In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of diverse r
Externí odkaz:
http://arxiv.org/abs/2309.13277