Results 51 to 60 of about 154,581 (190)
Explicit height estimates for CM curves of genus 2
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract In this paper, we make explicit the constants of Habegger and Pazuki's work from 2017 on bounding the discriminant of cyclic Galois CM fields corresponding to genus 2 curves with CM and potentially good reduction outside a predefined set of primes. We also simplify some of the arguments.
Linda Frey +2 more
wiley +1 more source
A density theorem in parametrized differential Galois theory [PDF]
Pacific Journal of Mathematics, 2014 To appear in Pacific Journal of ...
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Topological K‐theory of quasi‐BPS categories for Higgs bundles
Journal of Topology, Volume 18, Issue 4, December 2025.Abstract In a previous paper, we introduced quasi‐BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi‐BPS categories (called BPS in this case) are noncommutative analogues of Hitchin integrable systems.
Tudor Pădurariu, Yukinobu Toda
wiley +1 more source
On the section conjecture over fields of finite type
Mathematische Nachrichten, Volume 298, Issue 11, Page 3476-3493, November 2025.Abstract Assume that the section conjecture holds over number fields. We prove then that it holds for a broad class of curves defined over finitely generated extensions of Q$\mathbb {Q}$. This class contains every projective, hyperelliptic curve, every hyperbolic, affine curve of genus ≤2$\le 2$, and a basis of open subsets of any curve.
Giulio Bresciani
wiley +1 more source
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
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
, 2020 Galois Theory is a powerful tool to study the roots of polynomials. In this sense, the differential Galois theory is the analogue of Galois theory for linear differential equations. In this thesis, we will construct the notion of a differential field and Picard-Vessiot extension of a linear differential equation as the analogue of a field and the ...
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The inverse problem of differential Galois theory over the field R(z) [PDF]
, 2008 Tobias Dyckerhoff
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Poisson Groups and Differential Galois Theory of Schroedinger Equation on the Circle [PDF]
, 2008 Ian Marshall +1 more
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