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See also the related The use of embedding a curve into its Jacobian If you don't have access to Timo's reference there is also the free resource J.Stix On cuspidal sections of algebraic fundament …

Quoting Vistoli, Angelo Intersection theory on algebraic stacks and on their moduli spaces. Invent. Math. 97 (1989), no. 3, 613–670. to be found here http://dx.doi.org/10.1007/BF01388892 : Defini …

One can prove this correspondence along these lines : let $a: G\times X\rightarrow X$ be the action. A $G$-linearisation on a sheaf $\mathcal F$ consists of an isomorphism $a^*\mathcal F\simeq pr_2^*\ …

See Angelo Vistoli Intersection theory on algebraic stacks and on their moduli spaces Inventiones mathematicae (1989) Volume: 97, Issue: 3, page 613-670 EUDML  |  Intersection theory on algebraic stac …

see SGA1 http://arxiv.org/abs/math/0206203 Exposé V Corollaire 2.3

If I remember correctly, this goes roughly as follows. Consider the category $\mathcal C=\operatorname{Rings}^{op}$, first endowed with the Zariski topology. You can consider sheaves on this site that …

It depends on what you call Nori's fundamental group scheme, of course. Nori himself has given several versions of his fundamental group scheme, and it has been vastly generalized. If you think of th …

The source text Kato, Kazuya Logarithmic structures of Fontaine-Illusie. Algebraic analysis, geometry, and number theory (Baltimore, MD, 1988), 191–224, Johns Hopkins Univ. Press, Baltimore, MD, 1989 …

I think there is a complete answer to your question in SGA 6 Exp X $\S$ 5 : for a quasi-compact scheme there is a natural isomorphism (first Chern class) ${\rm Pic} X \simeq Gr^1(X)$ where $Gr^1(X)$ …

As Keerthi Madapusi Pera points out in his comments, it is certainly reasonable to define a unipotent flat vector bundle as a flat vector bundle that is a successive extension of the trivial one $(\m …

Claim : if $k$ is perfect of characteristic $0$, then : $$\mathbb Z^{k, alg}\simeq \mathbb G_a\times D_k(k^*)$$ Here $\mathbb Z^{k, alg}$ stands for the pro-algebraic completion of $\mathbb Z$ (the …

The best thing you could do in my opinion is to have a look at Appendix A Algebraic $K(\pi, 1)$ Spaces in Stix, Jakob Projective anabelian curves in positive characteristic and descent theory …

The proof given in Laumon and Moret-Bailly is clear and does not seem to use your claim. Denote by $G=\Delta_F :\mathcal X \to \mathcal X \times_{\mathcal Y} \mathcal X$ the diagonal morphism. The m …

The answer is "yes" I think, even if you replace $\mathbb Q$ with a number field. In the affine case this is a result of Matsumoto, as pointed out by Felipe Voloch, see Matsumoto, Makoto Galois rep …

When $X={\rm spec}\; k$, the spectrum of a field, your question seems to be related to (non neutral) Tannaka duality : gerbes over a field are characterized by they categories of representations (see …