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Revêtements étales et groupe fondamental (SGA 1)

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TLDR
In this paper, the fundamental group theory of algebraic geometry from the Kronecker point of view is presented, allowing one to treat on an equal footing the case of an algebraic variety in the usual sense and that of the ring of integers in a number field, for instance.
Abstract
Le texte pr\'esente les fondements d'une th\'eorie du groupe fondamental en G\'eom\'etrie Alg\'ebrique, dans le point de vue ``kroneckerien'' permettant de traiter sur le m\^eme pied le cas d'une vari\'et\'e alg\'ebrique au sens habituel, et celui d'un anneau des entiers d'un corps de nombres, par exemple. The text presents the foundations of a theory of the fundamental group in Algebraic Geometry from the Kronecker point of view, allowing one to treat on an equal footing the case of an algebraic variety in the usual sense, and that of the ring of integers in a number field, for instance.

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A theory of generalized Donaldson-Thomas invariants

Dominic Joyce, +1 more
TL;DR: In this article, generalized Donaldson-Thomas invariants are defined for all classes of coherent sheaves, and they are equal to $DT^\alpha(\tau)$ when it is defined.
Book

Central Simple Algebras and Galois Cohomology

TL;DR: The first comprehensive introduction to the theory of central simple algebras over arbitrary fields was given by Brauer, Noether, Hasse and Albert as mentioned in this paper, who also gave a proof of the Merkurjev-Suslin theorem.
Journal ArticleDOI

On the nonexistence of elements of Kervaire invariant one

TL;DR: In this article, it was shown that the Kervaire invariant one elements θj ∈ π2j+1−2S exist only for j ≤ 6.
Journal ArticleDOI

Homotopical algebraic geometry. I. Topos theory.

TL;DR: In this article, the notions of S-topologies, S-sites, and stacks over sites were introduced, and a model category of pre-stacks over a Grothendieck site was introduced.
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Framed bicategories and monoidal fibrations

TL;DR: In this paper, two ways to construct framed bicategories are described, one is an analogue of rings and bimodules, which starts from one framed category and builds another, and the other is a monoidal fibration, meaning a parametrized family of monoidal categories.