相关论文: On Hrushovski's proof of the Manin-Mumford conject…

We prove the following completeness result about classical realizability: given any Boolean algebra with at least two elements, there exists a Krivine-style classical realizability model whose characteristic Boolean algebra is elementarily…

We study the algbraic dynamics for endomorphisms of projective spaces with coefficients in a p-adic field whose reduction in positive characteritic is the Frobenius. In particular, we prove a version of the dynamical Manin-Mumford…

An elementary proof of a theorem of Montanucci and Zini on the automorphism group of generalized Aritn-Schreier-Mumford curves is presented, with the argument of Korchmaros and Montanucci for Artin-Schreier-Mumford curves being improved.…

Twisted Gromov-Witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold X which depend in addition on a vector bundle over X and an invertible multiplicative characteristic class. Special cases…

We present a simple set-theoretic proof of the Banach-Stone Theorem .We thus apply this Topological classification theorem to the still unsolved problem of topological classification of euclidean manifolds through two conjectures and…

In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel Surjection of the first paper in the series to relate…

We give a simplified proof of elimination of imaginaries (in the geometric sorts) in ACVF, based on ideas of Hrushovski. This proof manages to avoid many of the technical issues which arose in the original proof by Haskell, Hrushovski, and…

In this paper the surjective homomorphism from the Drinfeld realization to the Drinfeld and Jimbo presentation of affine quantum algebras is proved to be injective. A consequence of the arguments used in the paper is the triangular…

We consider the Zariski-Lipman Conjecture on free module of derivations for algebraic surfaces. Using the theory of non-complete algebraic surfaces, and some basic results about ruled surfaces, we will prove the conjecture for several…

First, we prove an algebraization result for rig-smooth algebras over a general noetherian ring; this positively answers the question raised in [Sta24, Tag 0GAX]. Then we prove a general partial algebraization result in non-archimedean…

We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…

We prove the thin set version of Manin's conjecture for the chordal (or: determinantal) cubic fourfold, which is the secant variety of the Veronese surface. We reduce this counting problem to a result of Schmidt for quadratic points in the…

In this paper we discuss metric theory associated with the affine (inhomogeneous) linear forms in the so called doubly metric settings within the classical and the mixed setups. We consider the system of affine forms given by $\qq\mapsto…

We discuss the Ribaucour transformation of Legendre maps in Lie sphere geometry. In this context, we give a simple conceptual proof of Bianchi's original Permutability Theorem and its generalisation by Dajczer--Tojeiro. We go on to…

We prove Kontsevich's homological mirror symmetry conjecture for a large class of mirror pairs of Calabi--Yau hypersurfaces in toric varieties. These mirror pairs were constructed by Batyrev from dual reflexive polytopes. The theorem holds…

In this paper, motivated by a problem posed by Barry Mazur, we show that for smooth projective varieties over the rationals, the odd cohomology groups of degree less than or equal to the dimension can be modeled by the cohomology of an…

Using the Galois theory over function field, and the holomorphy of algebroids defined via irreducible polynomial at singular points, we prove the injectivity of any kellerian mapping. The famous Jacobian conjecture is true.

Geometric Manin's conjecture predicts that components of the moduli space of curves on a Fano variety parametrizing non-free curves are pathological and arise from "accumulating" morphisms that increase the Fujita invariant. By passing to…

This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).

We generalize the definition of orbifold elliptic genus, and introduce orbifold genera of chromatic level h, using h-tuples rather than pairs of commuting elements. We show that our genera are in fact orbifold invariants, and we prove…