相关论文: Canonical extensions of N\'eron models of Jacobian…

We study the family of algebraic curves of genus $\geq 1$ defined by the affine equations $y^s=ax^r+b$ over a number field $k$, where $r \geq 2$ and $s\geq 2$ are fixed integers. Assuming the strong version of Lang's conjecture on varieties…

We consider slope stability of the canonical extension of the tangent bundle by the trivial line bundle and with the extension class c_1(T_X) on Picard-rank-1 Fano varieties. In cases where the index divides the dimension or the dimension…

Suppose $X$ is a hyperelliptic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p=2$. We prove that the de Rham cohomology of $X$ decomposes into pieces indexed by the branch points of the hyperelliptic…

For a semi-stable abelian variety A_K over a complete discrete valuation field K, we show that every finite subgroup scheme of A_K extends to a log finite flat group scheme over the valuation ring of K endowed with the canonical log…

For flat proper families of algebraic varieties with a smooth fiber, we describe the abelian category of coherent sheaves on the generic fiber as a Serre quotient. As an application, we prove specialization of derived equivalence. As…

A basic technique for studying a family of Jacobian varieties is to extend the family by adding degenerate fibers. Constructing an extension requires a choice of fibers, and one typically chooses to include either degenerate group varieties…

Let $X_0$ be an affine variety with only normal isolated singularity $p$ and $\pi: X\to X_0$ a smooth resolution of the singularity with trivial canonical line bundle $K_X$. If the complement of the affine variety $X_0\backslash\{p\}$ is…

We observe that general reducible curves in sufficiently positive linear systems on K3 surfaces are of a form that generalises Kodaira's classification of singular elliptic fibres and thus call them extended ADE curves. On such a curve $C$,…

The jacobian of the universal curve over $\mathcal{M}_{g,n}$ is an abelian scheme over $\mathcal{M}_{g,n}$. Our main result is the construction of an algebraic space $\beta\colon \tilde{\mathcal{M}}_{g,n} \rightarrow…

Let $X$ be a quasi-compact, separated scheme over a field k and we can consider the categorical resolution of singularities of $X$. In this paper let $k^{\prime}/k$ be a field extension and we study the scalar extension of a categorical…

We determine explicitly the Picard groups of the universal Jacobian stack and of its compactification over the stack of stable curves. Along the way, we prove some results concerning the gerbe structure of the universal Jacobian stack over…

Matrix pencils, or pairs of matrices, are used in a variety of applications. By the Kronecker decomposition Theorem, they admit a normal form. This normal form consists of four parts, one part based on the Jordan canonical form, one part…

In this article we prove new results on projective normality and normal presentation of adjunction bundle associated to an ample and globally generated line bundle on higher dimensional smooth projective varieties with nef canonical bundle.…

We show that algebraic equivalence of images of stable maps of curves lifts to deformation equivalence of the stable maps. The main applications concern $A_1(X)$, the group of 1-cycles modulo algebraic equivalence, for smooth, separably…

The K-theory of a functor may be viewed as a relative version of the K-theory of a ring. In the case of a Galois extension of a number field F/L with rings of integers A/B respectively, this K-theory of the "norm functor" is an extension of…

We contribute XTT, a cubical reconstruction of Observational Type Theory which extends Martin-L\"of's intensional type theory with a dependent equality type that enjoys function extensionality and a judgmental version of the unicity of…

We investigate the homological ideal $\mathfrak{J}_G^H$, the kernel of the restriction functors in compact Lie group equivariant Kasparov categories. Applying the relative homological algebra developed by Meyer and Nest, we relate the…

Graded Artinian algebras can be regarded as algebraic analogues of cohomology rings (in even degrees) of compact topological manifolds. In this analogy, a free extension of a base ring with a fiber ring corresponds to a fiber bundle over a…

Let $C$ be a smooth projective curve defined over a number field $k$, $X/k(C)$ a smooth projective curve of positive genus, $J_X$ the Jacobian variety of $X$ and $(\tau,B)$ the $k(C)/k$-trace of $J_X$. We estimate how the rank of…

We study the Jacobian conjecture for Keller maps $f:X_0:=\mathbf{A}^n\rightarrow Y_0:=\mathbf{A}^n$ in characteristic $0$ and attempt to prove it. We are quite aware of the fact that many people have tried to prove the Jacobian conjecture…