Papers nuevos sobre Álgebra y teoría de números
487 papers nuevos sobre álgebra y teoría de números en los últimos 7 días, dentro de Matemática y estadística. Acá están los 50 que Pipette considera más valiosos, con el resultado principal en palabras de sus autores.
Lo mejor de la semana
The Odlyzko-Poonen Conjecture on Irreducibility of Random Polynomials
We prove the Odlyzko-Poonen conjecture unconditionally.
PreprintDice ser un gran avanceInverse Baer deformations and finite simple skew braces of nilpotent type
Applying this construction to simple left braces arising from asymmetric products, for every pair of odd primes with and every we construct a finite simple skew brace of order such that \[ (X_{p,q}^{(m)},+)\cong E_{p,q}^{(m)}\times C_q, \] where is an extraspecial -group of order and exponent .
PreprintDice ser un gran avanceMathematical Principles of a Generalized Tonal Practice
We develop mathematical principles for a generalized tonal practice.
PreprintSolution to Dixmier's Problem about spectra of C*-algebras
We solve Dixmier's 1967 problem about spectra of simple -algebras.
PreprintDice ser un gran avanceReal quadratic fields and finite quantum dilogarithms I
We prove that Stark-Shintani ray class invariants (Stark units) associated to real quadratic fields are algebraic numbers.
PreprintAlt's Problem
We prove there are four-bar coupler curves through nine generic points in the plane, and thus resolve Alt's problem.
PreprintA Machine-Checked Proof that Gardam's Lattice Does Not Have Unique Products
We give a proof checked by the Lean 4 kernel and stated against Mathlib's UniqueProds class.
PreprintCódigo disponibleA separably representable counterexample to Naimark's problem in ZFC
We construct in ZFC a unital, simple, infinite-dimensional -algebra whose nonzero irreducible representations form a single unitary equivalence class, but which admits a faithful representation on a separable Hilbert space.
PreprintDice ser un gran avanceProof of the positive trace gap conjecture
We prove that a lattice in or has positive trace gap, meaning that its traces are uniformly separated, if and only if it is derived from an admissible quaternion algebra.
PreprintA solution to Michael's problem for Fr\'echet algebras
We prove that every character on a commutative complex complete Hausdorff locally multiplicatively convex algebra, not necessarily unital, is bounded on bounded sets.
PreprintDice ser un gran avanceOn -extensions of real quadratic fields with class group of -rank three
This gives the first example of an infinite family of real quadratic fields whose ideal class group has -rank three and whose cyclotomic -extension is totally ramified and satisfies Greenberg's conjecture.
PreprintDice ser un gran avanceOn low-discrepancy sequences and Poissonian pair correlation
As we prove in this paper, this is not the case: we construct an example of a low-discrepancy sequence with Poissonian pair correlation.
PreprintAffine Harish-Chandra center in positive characteristic
We identify the Harish--Chandra centers of the associated Kac--Moody vertex algebras and enveloping algebras at noncritical levels with algebras of functions on moduli spaces of connections for the Langlands dual group .
PreprintDice ser un gran avanceSuper adaptable graphs and the realization problem
Our main result shows that any countable super adaptable monoid can be realized by a von Neumann regular ring, thus answering affirmatively the Realization problem for this class.
PreprintDisproof of a Conjectured Upper Bound for the Davenport Constant
In this paper, we disprove this conjecture.
PreprintPoincar\'e Duality and Quadratic Refinements over Laurent Rings
We develop a Poincar\'e duality theory for defects of nondegenerate sesquilinear pairings over Laurent polynomial rings.
PreprintSome Infinite Families of Arithmetic Symplectic Hypergeometric Groups
Using the idea of Venkataramana's construction of infinite families of arithmetic orthogonal hypergeometric groups, we construct some of the very first examples of infinite families of arithmetic symplectic hypergeometric groups that do NOT satisfy the arithmeticity criterion of Singh and Venkataramana.
PreprintA proof of the irreducibility conjecture for Legendre polynomials
We prove the irreducibility conjecture for Legendre polynomials proposed by Stieltjes in his 1890 letter to Hermite.
PreprintThe Kazhdan-Lusztig category of at irrational levels
We prove the Kazhdan-Lusztig correspondence for the Lie superalgebra at irrational levels, that is, we show the category of finite-length even ordinary modules for the affine vertex operator superalgebra of at level is braided tensor equivalent to the category of finite-dimensional even weight modules for the quantum group of at parameter .
PreprintInterpolation determinants and the Lebesgue--Nagell equation
We prove the long-standing conjecture that, for every odd prime , the only integral solutions of are .
PreprintDegrees and directional defects of embedded algebraic vector bundles
As a main application, we establish the sharp universal bound for every smooth irreducible affine variety and its tangent bundle.
PreprintFixed point properties and cohomology of Banach representations of arithmetic groups
We show that for lattices in simple groups of higher rank, the cohomology with -coefficients vanishes below the rank whenever there are no invariant vectors.
PreprintHigh Rank and Multiplicity in Random and Perfect Profinite Groups
We prove that almost sure topological finite generation holds for a general class of random models of profinite groups.
Preprinthas the Bogomolov property for canonical heights
We show that for any number field and any rational map in that is not conjugate to a power, (signed) Chebyshev or Latt\`es map, then has the strong Bogomolov property for the canonical height of .
PreprintOn Haagerup-Izumi fusion categories
We prove the Evans-Gannon conjecture that the modular data of the center is always a smashed sum involving a finite metric group of order and recover this group and its quadratic form directly from the data of the HI category.
PreprintOn the Moufang condition for polar spaces
Consequently, we show that all thick polar spaces of finite and infinite rank are Moufang.
Preprint con versión publicadaA quasisymmetric analog of Grassmannian Schubert varieties
We show that the cohomology rings of toric Richardson varieties in the Grassmannian are finite truncations of the ring of quasisymmetric functions.
PreprintEuler characteristics of strata of -differentials
Our main result is a closed coefficient-extraction formula in terms of hyperbolic functions, valid for arbitrary strata and generalizing the Harer--Zagier formula for the Euler characteristic of the moduli space of curves.
PreprintA Secondary Multiplicative Structure on Lawson Homology
We introduce a new secondary operation on Lawson homology of smooth complex projective varieties.
PreprintA Peterson program for general Schubert varieties and mirror symmetry
We initiate a `Peterson program' that seeks to extend Dale Peterson's theory for the quantum cohomology of flag varieties to arbitrary Schubert varieties, and that incorporates a mirror-symmetric approach.
PreprintMonoidal Gr\"obner systems and categories of affine Brauer type
Our main result is a criterion for a category to be of affine Brauer type, reducing the question to an explicit list of local computations, which we partially implement in the computer algebra system FORM.
PreprintDetecting split surfaces, RM surfaces, and minimum walks on isogeny graphs
We develop algorithms to detect -splittings and to compute the minimum -splitting level of a superspecial Jacobian without constructing the corresponding isogeny path.
PreprintBeyond the unique pair: a two-parameter family of rational triangles with equal perimeter and area
Writing , we obtain a two-parameter description of the solutions and, for fixed , a family of curves which are generically of genus .
PreprintUniform Tur\'an estimates and sharp bounds for degree and mixed orbit growth
We prove that these exponents are coupled across three adjacent codimensions: strict log-concavity of at forces , while equality gives \[ 0\ \le\ 2\mu_i-\mu_{i-1}-\mu_{i+1}\ \le\ 4 .
PreprintLocally analytic representations in mixed characteristic via stacks
For any -adic Lie group , we construct a group stack over the -adic branch of Clausen--Scholze's stack of norms such that quasicoherent sheaves on its classifying stack recover locally analytic representations of after base change to any suitable Tate Huber pair, even in positive or mixed characteristic.
PreprintCounterexamples to the Reiner-Shimozono conjecture and the failure of Schubert filtrations
We disprove the Reiner--Shimozono conjecture that products of key polynomials have nonnegative expansions in Demazure atoms.
PreprintAlgebraically primitive Teichm\"uller curves in \Omega\mathcal M_g(2g-2)^{hyp}
We give a complete classification of algebraically primitive Teichm\"uller curves in for .
PreprintBrill-Noether existence with secants
Our main theorem shows that the natural necessary conditions are in fact sufficient, yielding a generalization of the classical Brill-Noether existence theorem.
PreprintStable base change from unitary groups in three variables and integral relation of automorphic periods
We prove a -adic divisibility between the automorphic periods of a cuspidal automorphic representation of and the periods of its Rogawski stable base change to .
PreprintSquaring Up by Selection: NP-Completeness at Three Simple Roots
We show that deciding whether a safe choice exists is NP-complete, already for an explicit family of systems of degree three with radical ideal and exactly three simple rational solutions.
PreprintComputing the cohomology of Shimura curves in quasi-linear time
Relying on work of Imbert, we leverage topological techniques to obtain linear systems so structured that they can be solved in time quasi-linear in the genus.
Preprint con versión publicadaThe unique extremal threemodular lattice of rank 26, the generalized hexagon , and the tight Cayley-plane -design
We reconstruct the generalized hexagon of order from an abstract even rank- lattice of determinant and minimum , and conversely reconstruct the lattice from the hexagon.
PreprintEqual subset sums and close divisors
We prove that , resolving a conjecture of Ford, Green and Koukoulopoulos [Invent. Math. 232 (2023), 1027--1160].
PreprintOn the generation of multiplicative groups by small primes
We prove that, for every fixed and , there is an absolute constant and a set of at most primes, all at most , such that for all but (with the implied constant depending only on and ) integers , every element of is a product of a subset of these primes modulo .
PreprintCollision Positivity for Three-Variable Symmetric Monomial Inequalities
We prove a necessary and sufficient collision criterion for the positivity of this three-point majorization difference in three variables.
PreprintThe Primitive Generalized Fermat Equation x^3+y^5=z^7: A computer-assisted proof
We prove that the generalized Fermat equation has no solution in nonzero coprime integers, and we make explicit how the proof extends the prior work cited below.
PreprintCódigo disponibleRank-two Nahm sums, modularity obstructions, and the McKay--Thompson series
We conjecture a positive four-shift identity for rank-two Nahm sums with denominator steps , giving a mixed-base realization of the Monster McKay--Thompson series through the classical Rogers--Ramanujan function .
Preprintp-curvature in non-commutative Hodge theory and the Kontsevich-Soibelman operad
Our main result is that when is smooth and proper, this connection has a regular singularity at and quasi-unipotent monodromy, affirming a conjecture of Katzarkov-Kontsevich-Pantev \cite{KKP}.
PreprintSingle-Orbit Recovery of Groups via an Optimization Principle
Our main result identifies a short list of conditions on a family of orthogonal matrices that force the family to be the right regular representation of a finite group.
PreprintNoncongruence cusp forms, Veech groups and enumeration
We prove the existence of weight 2 modular forms for some Veech groups, whose Fourier coefficients at a cusp determine the counts of numbers of branched Galois covers of punctured elliptic curves.
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