Results 51 to 60 of about 16,779 (193)

Arithmetic sparsity in mixed Hodge settings

Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3511-3521, November 2025.
Abstract Let X$X$ be a smooth irreducible quasi‐projective algebraic variety over a number field K$K$. Suppose X$X$ is equipped with a p$p$‐adic étale local system compatible with an admissible graded‐polarized variation of mixed Hodge structures on the complex analytification of XC$X_{\operatorname{\mathbb {C}}}$.
Kenneth Chung Tak Chiu
wiley   +1 more source

Algebraic D-groups and differential Galois theory [PDF]

Pacific Journal of Mathematics, 2004
The author gives another exposition of his new differential Galois theory. As he thinks, a previous presentation [Ill. J. Math. 42, No. 4, 678--699 (1998; Zbl 0916.03028)] was too model-theoretic and so somewhat obscure to differential algebraists. This new representation is based on some generalization of \(G\)-primitive extensions of \textit{E.
openaire   +2 more sources

The geometry and arithmetic of bielliptic Picard curves

Journal of the London Mathematical Society, Volume 112, Issue 5, November 2025.
Abstract We study the geometry and arithmetic of the curves C:y3=x4+ax2+b$C \colon y^3 = x^4 + ax^2 + b$ and their associated Prym abelian surfaces P$P$. We prove a Torelli‐type theorem in this context and give a geometric proof of the fact that P$P$ has quaternionic multiplication by the quaternion order of discriminant 6.
Jef Laga, Ari Shnidman
wiley   +1 more source

A note on local formulae for the parity of Selmer ranks

Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3112-3132, October 2025.
Abstract In this note, we provide evidence for a certain ‘twisted’ version of the parity conjecture for Jacobians, introduced in prior work of Dokchitser, Green, Konstantinou and the author. To do this, we use arithmetic duality theorems for abelian varieties to study the determinant of certain endomorphisms acting on p∞$p^\infty$‐Selmer groups.
Adam Morgan
wiley   +1 more source

Galois Theory of Parameterized Differential Equations and Linear Differential Algebraic Groups

, 2005
We present a Galois theory of parameterized linear differential equations where the Galois groups are linear differential algebraic groups, that is, groups of matrices whose entries are functions of the parameters and satisfy a set of differential ...
Cassidy, Phyllis J., Singer, Michael F.
core   +2 more sources

Toward quantized Picard-Vessiot theory, Further observations on our previous example [PDF]

, 2013
It is quite natural to wonder whether there is a difference-differential equations, the Galois group of which is a quantum group that is neither commutative nor co-commutative.
Saito, Katsunori, Umemura, Hiroshi
core  

The relative Hodge–Tate spectral sequence for rigid analytic spaces

Journal of the London Mathematical Society, Volume 112, Issue 4, October 2025.
Abstract We construct a relative Hodge–Tate spectral sequence for any smooth proper morphism of rigid analytic spaces over a perfectoid field extension of Qp$\mathbb {Q}_p$. To this end, we generalise Scholze's strategy in the absolute case by using smoothoid adic spaces.
Ben Heuer
wiley   +1 more source

The inverse problem of differential Galois theory over the field R(z)

, 2007
We describe a Picard-Vessiot theory for differential fields with non algebraically closed fields of constants. As a technique for constructing and classifying Picard-Vessiot extensions, we develop a Galois descent theory.
Dyckerhoff, Tobias
core   +1 more source

Galois theory of differential fields of positive characteristic [PDF]

Pacific Journal of Mathematics, 1989
Strongly normal extensions of a differential field \(K\) of positive characteristic are defined. On the set \(G\) of all differential isomorphisms of a strongly normal extension \(N\) of \(K\), a structure of an algebraic group is induced. Correspondences between subgroups of \(G\) and intermediate differential fields of \(N\) and \(K\) are studied ...
openaire   +3 more sources

Fractional moments of L$L$‐functions and sums of two squares in short intervals

Mathematika, Volume 71, Issue 4, October 2025.
Abstract Let b(n)=1$b(n)=1$ if n$n$ is the sum of two perfect squares, and b(n)=0$b(n)=0$ otherwise. We study the variance of B(x)=∑n⩽xb(n)$B(x)=\sum _{n\leqslant x}b(n)$ in short intervals by relating the variance with the second moment of the generating function f(s)=∑n=1∞b(n)n−s$f(s)=\sum _{n=1}^{\infty } b(n)n^{-s}$ along Re(s)=1/2$\mathrm{Re}(s)=1/
Siegfred Baluyot, Steven M. Gonek
wiley   +1 more source