Related papers: A Lefschetz-Riemann-Roch theorem for singular sche…

Via a construction due to V. Drinfel'd, we prove an equivalence of categories, generalizing the equivalence between commutative flat group schemes in characteristic $p$ with trivial Verschiebung and their Dieudonn\'e modules to group…

We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K_0 of the category of "phi-endomorphisms of finitely generated free…

The purpose of this article is to present a "Groupoid proof" to the Lefschetz fixed point formula for elliptic complexes. We shall define a "relative version" of tangent groupoid, describe the corresponding pseudodifferential calculi and…

Kobayashi-Ochiai's theorem says us that the set of dominant rational maps to a complex variety of general type is finite. In this paper, we give a generalization of it in the category of log schemes.

We prove a Riemann-Roch theorem for real divisors on edge-weighted graphs over the reals, extending the result of Baker and Norine for integral divisors on graphs with multiple edges.

Let $S$ be a complex projective surface. Lefschetz originally proved Lefschetz $(1, 1)$--Theorem by studying a Lefschetz pencil of hyperplane sections of $S$ and the Abel--Jacobi mapping. In this paper, we attack Lefschetz $(1, 1)$--Theorem…

Given a vector bundle $F$ on a smooth Deligne-Mumford stack $\X$ and an invertible multiplicative characteristic class $\bc$, we define the orbifold Gromov-Witten invariants of $\X$ twisted by $F$ and $\bc$. We prove a "quantum Riemann-Roch…

A Riemann-Roch theorem on graph was initiated by M. Baker and S. Norine. In their article [2], a Riemann-Roch theorem on a finite graph with uniform vertex-weight and uniform edge-weight was established and it was suggested a Riemann-Roch…

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

Any smooth, projective variety satisfies the Hodge conjecture in codimension one, known as the Lefschetz (1,1) theorem. Totaro formulated a version for singular varieties. He asked whether the natural Bloch-Gillet-Soul\'{e} cycle class map…

We develop a method for proving the Boone--Higman Conjecture for groups acting on locally finite trees. As a consequence, we prove the Boone--Higman Conjecture for all Baumslag--Solitar groups and for all free(finite rank)-by-cyclic groups,…

We prove a theorem of Tits type for automorphism groups of projective varieties over an algebraically closed field of arbitrary characteristic, which was first conjectured by Keum, Oguiso and Zhang for complex projective varieties.

We study the actions of a Lie group $G$ by birationally extendible automorphisms on a domain $D\subset C^n$. For a large class of such domains defined by polynomial inequalities, all automorphisms are of this type. In the cases 1) $G$ has…

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products…

We consider a generalized Riemann-Hurwitz formula as it may be applied to rational maps between projective varieties having an indeterminacy set and fold-like singularities. The case of a holomorphic branched covering map is recalled. Then…

A $G$-invariant version of definable Tietze extension theorem for definably complete structures is proved when a definably compact definable topological group $G$ acts definably and continuously on the definable set.

We describe the standard and Leray filtrations on the cohomology groups with compact supports of a quasi projective variety with coefficients in a constructible complex using flags of hyperplane sections on a partial compactification of a…

We prove the classical Riemann-Roch theorems for the Adams operations $\,\psi^j\,$ on $K$-theory: a statement with coefficients on $\mathbb{Z}[j^{-1}]$, that holds for arbitrary projective morphisms, as well as another one with integral…

We prove the hard Lefschetz theorem and the Hodge-Riemann relations for a commutative ring associated to an arbitrary matroid M. We use the Hodge-Riemann relations to resolve a conjecture of Heron, Rota, and Welsh that postulates the…