Results 31 to 40 of about 5,607,191 (74)
, 1972 The purpose of this thesis is to examine the correspondence between groups of automorphsims and fields and to prove the Fundamental Theorem of Galois Theory. The fields under consideration are infinite.
Mastin, Millicent Gay +1 more
core
Symmetric products and puncturing Campana‐special varieties
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract We give a counterexample to the Arithmetic Puncturing Conjecture and Geometric Puncturing Conjecture of Hassett–Tschinkel using symmetric powers of uniruled surfaces, and propose a corrected conjecture inspired by Campana's conjectures on special varieties.
Finn Bartsch +2 more
wiley +1 more source
Periodic points of rational functions over finite fields
Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.Abstract For q$q$ a prime power and ϕ$\phi$ a rational function with coefficients in Fq$\mathbb {F}_q$, let p(q,ϕ)$p(q,\phi)$ be the proportion of P1Fq$\mathbb {P}^1\left(\mathbb {F}_q\right)$ that is periodic with respect to ϕ$\phi$. Furthermore, if d$d$ is a positive integer, let Qd$Q_d$ be the set of prime powers coprime to d!$d!$ and let P(d,q ...
Derek Garton
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
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
Artin L-Functions for Abelian Extensions of Imaginary Quadratic Fields [PDF]
, 2005 Let F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers.
Johnson, Jennifer Michelle
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Parity of ranks of Jacobians of curves
Proceedings of the London Mathematical Society, Volume 131, Issue 3, September 2025.Abstract We investigate Selmer groups of Jacobians of curves that admit an action of a non‐trivial group of automorphisms, and give applications to the study of the parity of Selmer ranks. Under the Shafarevich–Tate conjecture, we give an expression for the parity of the Mordell–Weil rank of an arbitrary Jacobian in terms of purely local invariants ...
Vladimir Dokchitser +3 more
wiley +1 more source
Hasse principle for Kummer varieties in the case of generic 2‐torsion
Proceedings of the London Mathematical Society, Volume 131, Issue 1, July 2025.Abstract Conditional on finiteness of relevant Shafarevich–Tate groups, Harpaz and Skorobogatov used Swinnerton‐Dyer's descent‐fibration method to establish the Hasse principle for Kummer varieties associated to a 2‐covering of a principally polarised abelian variety under certain largeness assumptions on its mod 2 Galois image.
Adam Morgan
wiley +1 more source
On piecewise trivial Hopf—Galois extensions [PDF]
, 2006 We discuss a noncommutative generalization of compact principal bundles that can be trivialized relative to the finite covering by closed sets.
Zieliński, B., Kraehmer, U.
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On the Galois correspondence theorem in separable Hopf Galois theory [PDF]
, 2019 In this paper we present a reformulation of the Galois correspondence theorem of Hopf Galois theory in terms of groups carrying farther the description of Greither and Pareigis.
Vela del Olmo, Ma. Montserrat +2 more
core +3 more sources