2549 papers
This paper utilizes complex cobordism to demonstrate that minimal cohomology classes on the Jacobians of very general curves provide new examples of algebraic integral cohomology classes that cannot be expressed as integral linear combinations of classes of smooth subvarieties, with the lowest possible dimension for such counterexamples being six.
This paper establishes necessary and sufficient conditions for the good reduction of Kummer surfaces associated with abelian surfaces having non-supersingular reduction over a perfect field of characteristic 2, demonstrating that such reduction admits an explicit scheme model equivalent to an algebraic space model.
This paper investigates the arithmetic geometry of the reduction modulo of the Siegel modular variety with parahoric level structure by realizing its EKOR-stratification as the fibers of a smooth morphism into an algebraic stack parametrizing homogeneously polarized chains of truncated displays.
This paper establishes the generalized Hodge, motivated Mumford-Tate, and generalized Tate conjectures for all complex Gushel-Mukai varieties, computes their integral Chow groups (with two specific exceptions), and proves that generalised partners or duals possess isomorphic rational Chow motives in middle degree.
This paper investigates the distribution of -smooth polynomials over finite fields with prescribed coefficients by employing character sum estimates, adapting Bourgain's argument, and analyzing double character sums.
This paper constructs a large family of pairwise non-isomorphic hyperelliptic curves mapping birationally into abelian surfaces isogenous to products of elliptic curves to generate rational equivalences in the Chow group of zero-cycles, thereby providing progress toward Beilinson's conjecture on the vanishing of the kernel of the Albanese map.
This paper provides a complete description of the Poisson boundary for wreath products under conditions where lamp configurations stabilize and the projected measure on is Liouville, thereby resolving a long-standing open question regarding the boundary for () with finite first moment measures.
Inspired by Pan's work, this paper provides a new proof that an overconvergent modular eigenform of weight $1+kp$, achieved by demonstrating that the theta operator coincides with the Fontaine operator.
This paper establishes a general framework for visible Lagrangians in Hitchin systems that factor through proper subvarieties of the Hitchin base, computes their fiber-wise Fourier-Mukai transforms to construct mirror dual branes, and provides a detailed new example arising from pillowcase covers that connects to Hausel's toy model.
This paper establishes a complete time-harmonic scattering theory for hyperbolic space by introducing a hyperbolic Sommerfeld radiation condition and Rellich theorem to uniquely define far-field patterns, thereby solving direct scattering problems and initiating the study of inverse scattering for obstacles and media in this geometry.
This paper introduces the non-commutative Group Ring Learning with Errors () problem based on semi-direct products of cyclic groups and establishes its cryptographic security by providing polynomial-time quantum reductions from the worst-case Shortest Independent Vectors Problem () to both the search and decision versions of .
This paper generalizes the local-relative correspondence beyond maximal contacts by identifying genus zero relative Gromov–Witten invariants of a smooth projective variety with a smooth nef divisor against specific orbifold invariants of multi-root stacks over a -bundle, thereby enabling the computation of relative invariants via absolute invariants of toric bundles.
The paper demonstrates that every Hardy field can be extended to an -free Hardy field, a result that connects to classical oscillation criteria and is used to resolve questions posed by Boshernitzan and generalize one of his theorems.
This paper establishes that the normal Lebesgue trace satisfies the Gauss-Green identity and occupies an intermediate regularity class between distributional and strong traces, enabling the proof of uniqueness for weak solutions to continuity equations on bounded domains under relaxed boundary regularity assumptions, while demonstrating that such assumptions remain necessary when characteristics enter the domain.
This paper investigates how key properties of probability monads, including their Kleisli laws, monoidal structures, and affinity, arise from their codensity presentations, establishing new universal properties for these monads and characterizing their tensor products via Day convolution while highlighting the limitations of the Giry monad on standard Borel spaces.
This paper investigates the contact process on dynamical random trees with degree-dependent edge updates, establishing sufficient conditions for a positive critical infection rate on general graphs and characterizing phase transitions—specifically proving strong survival for any infection rate under certain offspring distributions and providing a complete phase transition analysis for power-law trees with product kernels.
This paper introduces the Alternating Subspace Method (ASM), a novel sparse recovery algorithm that integrates greedy and splitting strategies by enforcing data fidelity within a subspace, thereby guaranteeing global convergence and achieving fast local geometric convergence on LASSO problems while demonstrating high efficiency and flexibility across various applications.
This paper demonstrates that while the direct sum of general representable -matroids is not necessarily representable, the direct sum of uniform -matroids is always representable over a sufficiently large field, a result established through algebraic and geometric tools involving cyclic flats.
This paper investigates the horofunction boundaries of Carnot groups by proving that all horofunctions are piecewise-defined via Pansu derivatives and demonstrating that filiform Lie groups of dimension provide the first examples where the boundary dimension deviates from the expected .
This paper revisits and improves upon Erdős and Rado's proof regarding well-quasi-ordered finite-image sequences of length to establish that the maximum linearization of such sequences is bounded by a function roughly -times exponential in the maximum linearization of the underlying well-quasi-order, a bound shown to be nearly tight for .