Related papers: Champs alg\'ebriques et foncteur de Picard

Isabelle/PIDE has emerged over more than 10 years as the standard Prover IDE for interactive theorem proving in Isabelle. The well-established Archive of Formal Proofs (AFP) testifies the success of such applications of formalized…

After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a…

Long ago, Fontaine formulated conjectures (now theorems) relating \'etale and de Rham cohomologies of algebraic varieties over $p$-adic fields. In an earlier work we have shown that pro-\'etale and de Rham cohomologies of analytic varieties…

An idea of Hopf's for applying complex analysis to the study of constant mean curvature spheres is generalized to cover a wider class of spheres, namely, those satisfying a Weingarten relation of a certain type, namely H = f(H^2-K) for some…

The purpose of this short note is to establish the existence of $\partial$-parameterized Picard-Vessiot extensions of systems of linear difference-differential equations over difference-differential fields with algebraically closed…

In this paper we present a more transparent upgrade of our proofs and comment on Jerabek's paper [8].

This submission has been withdrawn by arXiv administration.

This paper has been withdrawn - the results (with updated proofs) now appear in arXiv:0801.1627.

The Isabelle Archive of Formal Proofs has grown to a significant size in the past years. It makes up for an impressive body of research, which enables a number of statistical approaches to various aspects in theorem proving, and has not yet…

This paper has been withdrawn by the authors for adding some results.

Cohomology of a topological space with coefficients in stacks of abelian 2-groups is considered. A 2-categorical analog of the theorem of Grothendieck is proved, relating cohomology of the space with coefficients in a 2-stage spectrum and…

Those are notes of a mini-course the author gave in July 2010 at the university Paris 6 (Jussieu) during the summer school of the ANR (Agence nationale de la recherche) BERKO.

In the present paper, we study a relation between the cohomology of moduli stacks of smooth and proper curves $\mathcal M_{g,n}$ and the cohomology of ribbon graph complexes. The main results of this work are proofs of T. Willwacher's…

In this paper we give a construction of algebraic (Artin) stacks endowed with a modular map onto the moduli stack of n-pointed stable curves of genus g, for g greater than 2. These stacks are smooth, irreducible and have dimension 4g-3+n,…

We define a category whose objects are finite etale coverings of an algebraic stack and prove that it is a Galois category and that it allows one to compute the fundamental group of the stack. We then prove a Van Kampen theorem for…

This is the final version of the 2007 preprint titled "On the derived category of 1-motives, I". It has been substantially expanded to contain a motivic proof of (two thirds of) Deligne's conjecture on 1-motives with rational coefficients,…

We develop a basic theory of cocartesian fibrations between Segal spaces (in line with that of arxiv:2102.05190), and use it to provide a proof of a theorem of Barwick (the main result of arxiv:1404.0108). Note: This work was originally the…

These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations…

We review (non-abelian) extensions of a given Lie algebra, identify a 3-dimensional cohomological obstruction to the existence of extensions. A striking analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi…

We give a rigorous mathematical proof for the validity of the toric sheaf cohomology algorithm conjectured in the recent paper by R. Blumenhagen, B. Jurke, T. Rahn, and H. Roschy (arXiv:1003.5217). We actually prove not only the original…