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        Questions tagged [ag.algebraic-geometry]

        for questions on algebraic geometry, including algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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        Forcing quasi-compactness

        I wonder what kind of conditions on a morphism of schemes imply, in a non-trivial fashion, quasi-compactness of the morphism. Some examples Finiteness of surjective etale morphisms Is a universally ...
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        Serre functors for non-proper categories

        One usually defines a Serre functor to be a functor on a $k$-linear category $\mathcal{C}$ which has finite dimensional $Hom$s over $k$. In that case, the standard definition is that a Serre functor $...
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        Generalization of a result of Frey

        In Proposition (2) in the paper [1], in below, it is proved that: Assume that $K$ is a number field and that $C$ has infinitely many points of degree $\leq d$ over $K$. (Here $d\geq 2$ is an integer)...
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        Cohomological flatness in spectral algebraic geometry

        If $f:X\rightarrow \mathrm{Spec}\,R$ is a proper, flat, cohomologically flat in degree 0 morphism of schemes with Noetherian target, then $O_X(X)$ is a flat $R$-module. Now if we switch to the world ...
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        19 views

        Hyperelliptic Jacobians with (or without) CM

        Let $C$ be a hyperelliptic curve $y^2 = f(x) $ defined over $\mathbb{Q}$, where $f(x) \in \mathbb{Q} [x]$ is a polynomial of degree $n=5$ or $6$, and $J = Jac(C)$ its Jacobian. I know Zarhin's result [...
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        Contractible affine surfaces of log Kodaira dimension 2

        The first examples of contractible smooth affine algebraic surfaces (over the complex numbers) of log Kodaira dimension 2 were constructed in a famous paper of Ramanujam https://www.jstor.org/stable/...
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        Holomorphic conformal structures on Hirzebruch surfaces

        Let $X$ be a complex surface. A generalized holomorphic conformal structure on $X$ is given by a tensor $\omega\in H^0(X, Sym^2\Omega^1_X\otimes L)$, where $L$ is a line bundle. Taking determinants ...
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        Equivariant Sheaf: Explanation on Stalks

        I have a question about the explanation of the data defining a so called equivariant sheaf $F$ on a scheme X from wiki: https://en.wikipedia.org/wiki/Equivariant_sheaf. Let denote by $\sigma: G \...
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        133 views

        Is this unipotent group, over characteristic 2, connected?

        Let $E_{ij}(x)\in \mathrm{Mat}_{7\times7}(\overline{\mathbb{F}}_2)$ be the matrix with zeros everywhere, except for the value $x$ at $ij$. Set $$a(x)=1+E_{12}(x)+E_{34}(x)+E_{56}(x),\quad b(y)=1+E_{23}...
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        Equivalence De Rham and Dolbeault groupoids

        I believe there is an error or incompleteness in Goldman's and Xia's proof of the equivalence of the De Rham and Dolbeault groupoids, contained in Rank One Higgs Bundles and Representations of ...
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        85 views

        Flat cohomology and finite direct sum

        Let $X$ be a scheme (we can assume $X$ is smooth over a field $k$). Let $\mathcal F_1$ and $\mathcal F_2$ be two sheaves of abelian groups on $X$. Is it always true that $H^i_{\text{flat}}(X, \...
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        102 views

        A proper flat family with geometrically reduced fibers

        Let $R$ be a Noetherian commutative unital ring. Let $f:X\rightarrow Y=\mathrm{Spec}\,R$ be a proper flat morphism of schemes with geometrically reduced fibers. We want to prove that the induced map $...
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        94 views

        Infinitesimal deformation of strict transform

        Let $X$ be an affine, complex surface with isolated singularities and $\pi:\widetilde{X} \to X$ be a resolution of singularities (not necessarily minimal) i.e., $\widetilde{X}$ is non-singular and $\...
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        EGA I (Springer), Proposition 0.4.5.4 [on hold]

        I do not understand one argument in the proof of Proposition 0.4.5.4. in the new version by Springer of EGA I. When proving that the functor $F$ is representable by $(X, \xi)$, where we obtained $X$ ...
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        115 views

        Fundamental group of the Grothendieck ring scheme

        Let $K_0(V_k)$ be the Grothendieck ring of $k$-varieties with $k$ a field. Let S$_k$ be its affine scheme. Is this a connected scheme for any field ? (I understand that this could be a very naive ...

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        山西福彩快乐十分钟
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