Related papers: Neron models of 1-motives and duality

Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelian categories with enough projective objects or enough…

Grothendieck proved in EGA IV that if any integral scheme of finite type over a locally noetherian scheme X admits a desingularization, then X is quasi-excellent, and conjectured that the converse is probably true. We prove this conjecture…

The goal of this paper is to introduce Hodge 1-motives of algebraic varieties and to state a corresponding cohomological Grothendieck-Hodge conjecture, generalizing the classical Hodge conjecture to arbitrarily singular proper schemes.

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for…

This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular, it is shown that motives with rational…

We explain some recent developments in the theory of Neron models for families of Jacobians associated to variations of Hodge structures of weight -1.

In the arithmetic of function fields Drinfeld modules play the role that elliptic curves take on in the arithmetic of number fields. As higher dimensional generalizations of Drinfeld modules, and as the appropriate analogues of abelian…

Let $A_K$ be an Abelian variety over the quotient field of a Dedekind domain $R$. We show that the identity component of the N\'eron model of $A_K$ acts regularly on any minimal model of $A_K$ over $R$, and discuss when the N\'eron model is…

Let S be a connected scheme smooth and of finite type over the field of complex numbers. To every 1-motive over S, Andr\'e associated the enriched Hodge realization given by a torsion-free, graded-polarizable and admissible variation of…

Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…

This paper has been superseded to a great extent by the following: Paper: math.AG/0511558 Title: The Neron-Severi group of a proper seminormal complex variety Authors: L. Barbieri-Viale, A. Rosenschon & V. Srinivas Paper: math.AG/0102150…

We define model category structures on the category of chain complexes over a Grothendieck abelian category depending on the choice of a generating family, and we study their behaviour with respect to tensor products and stabilization. This…

We introduce a new category of non-archimedean analytic spaces over a complete discretely valued field. These spaces, which we call uniformly rigid, may be viewed as classical rigid-analytic spaces together with an additional uniform…

Over a scheme of finite type over a field of characteristic zero, we prove that Nori an Voevodsky categories of relative Artin motives, that is the full subcategories generated by the motives of \'etale morphisms in relative Nori and…

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate…

We present here a relationship among massive self-dual models for spin-3 particles in $D=2+1$ via the Noether Gauge Embedment $(NGE)$ procedure. Starting with a first order model (in derivatives) $S_{SD(1)}$ we have obtained a sequence of…

A formalism of arithmetic partial differential equations (PDEs) is being developed in which one considers several arithmetic differentiations at one fixed prime. In this theory solutions can be defined in algebraically closed p-adic fields.…

In this paper we obtain a Poitou-Tate exact sequence for finite and flat group schemes over a global function field. We also extend the duality theorems for 1-motives over number fields obtained by D.Harari and T.Szamuely to the function…

We define 1-motives of a variety X over a perfect field of positive characteristic which realize the etale cohomology groups of X in dimension and codimension one. This is the analogue in positive characteristic of previous results of…

This paper studies the homotopy theory of the Grothendieck construction using model categories and semi-model categories, provides a unifying framework for the homotopy theory of operads and their algebras and modules, and uses this…