Results 21 to 30 of about 49 (48)
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
PBW Deformations of Smash Products Involving Hopf Algebra of Kac–Paljutkin Type
Journal of Mathematics, Volume 2025, Issue 1, 2025.Let H2n2 be the Kac–Paljutkin–type Hopf algebra of dimension 2n2, A its graded Koszul Artin–Schelter regular H2n2‐module algebra of Dimension 2, A! the Koszul dual of A, and Acop the braided‐opposite algebra of A. This paper describes (0, 1)‐degree PBW deformations of the smash product A♯H2n2 and those of A!♯H2n2 under the condition that the Koszul ...
Yujie Gao, Shilin Yang, Naihuan Jing
wiley +1 more source
Reflecting perfection for finite‐dimensional differential graded algebras
Bulletin of the London Mathematical Society, Volume 56, Issue 12, Page 3689-3707, December 2024.Abstract We generalise two facts about finite‐dimensional algebras to finite‐dimensional differential graded algebras. The first is the Nakayama lemma and the second is that the simples can detect finite projective dimension. We prove two dual versions which relate to Gorenstein differential graded algebras and Koszul duality, respectively.
Isambard Goodbody
wiley +1 more source
L${L}$‐functions of Kloosterman sheaves
Proceedings of the London Mathematical Society, Volume 129, Issue 5, November 2024.Abstract In this article, we study a family of motives Mn+1k$\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves constructed by Fresán, Sabbah, and Yu. They demonstrated that for n=1$n=1$, the L$L$‐functions of M2k$\mathrm{M}_{2}^k$ extend meromorphically to C$\mathbb {C}$ and satisfy the functional equations conjectured by ...
Yichen Qin
wiley +1 more source
A functorial approach to monomorphism categories II: Indecomposables
Proceedings of the London Mathematical Society, Volume 129, Issue 4, October 2024.Abstract We investigate the (separated) monomorphism category mono(Q,Λ)$\operatorname{mono}(Q,\Lambda)$ of a quiver over an Artin algebra Λ$\Lambda$. We show that there exists an epivalence (called representation equivalence in the terminology of Auslander) from mono¯(Q,Λ)$\overline{\operatorname{mono}}(Q,\Lambda)$ to rep(Q,mod¯Λ)$\operatorname{rep}(Q,\
Nan Gao +3 more
wiley +1 more source
Unified invariant of knots from homological braid action on Verma modules
Proceedings of the London Mathematical Society, Volume 128, Issue 5, May 2024.Abstract We re‐build the quantum sl(2)${\mathfrak {sl}(2)}$ unified invariant of knots F∞$F_{\infty }$ from braid groups' action on tensors of Verma modules. It is a two variables series having the particularity of interpolating both families of colored Jones polynomials and ADO polynomials, that is, semisimple and non‐semisimple invariants of knots ...
Jules Martel, Sonny Willetts
wiley +1 more source
Extendible functions and local root numbers: Remarks on a paper of R. P. Langlands
Mathematische Nachrichten, Volume 297, Issue 2, Page 741-782, February 2024.Abstract This paper refers to Langlands' big set of notes devoted to the question if the (normalized) local Hecke–Tate root number Δ=Δ(E,χ)$\Delta =\Delta (E,\chi )$, where E is a finite separable extension of a fixed nonarchimedean local field F, and χ a quasicharacter of E×$E^\times$, can be appropriately extended to a local ε‐factor εΔ=εΔ(E,ρ ...
Helmut Koch, Ernst‐Wilhelm Zink
wiley +1 more source
A p$p$‐adic approach to the existence of level‐raising congruences
Proceedings of the London Mathematical Society, Volume 128, Issue 2, February 2024.Abstract We construct level‐raising congruences between p$p$‐ordinary automorphic representations, and apply this to the problem of symmetric power functoriality for Hilbert modular forms. In particular, we prove the existence of the nth$n\text{th}$ symmetric power lift of a Hilbert modular eigenform of regular weight for each odd integer n=1,3,⋯,25$n =
Jack A. Thorne
wiley +1 more source
Arithmetics of homogeneous spaces over p$p$‐adic function fields
Journal of the London Mathematical Society, Volume 109, Issue 1, January 2024.Abstract Let K$K$ be the function field of a smooth projective geometrically integral curve over a finite extension of Qp$\mathbb {Q}_p$. Following the works of Harari, Scheiderer, Szamuely, Izquierdo, and Tian, we study the local–global and weak approximation problems for homogeneous spaces of SLn,K$\textrm {SL}_{n,K}$ with geometric stabilizers ...
Nguyen Manh Linh
wiley +1 more source
Some of the next articles are maybe not open access.
Examples of Non-Semisimple Hopf Algebra Actions on Artin-Schelter Regular Algebras
Algebras and Representation Theory, 2022Hui-Xiang Chen +2 more
exaly