Moduli stacks for diagrams of λ-connections are constructed and proven algebraic when the base is a smooth projective scheme over an algebraically closed field of characteristic zero.
arXiv preprint arXiv:1104.4828 , year=
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
In this paper, we give an expository account of the geometric properties of the moduli stack of $G$-bundles. For $G$ an algebraic group over a base field and $X \to S$ a flat, finitely presented, projective morphism of schemes, we give a complete proof that the moduli stack $Bun_G$ is an algebraic stack locally of finite presentation over $S$ with schematic, affine diagonal. In the process, we prove some properties of $BG$ and Hom stacks. We then define a level structure on $Bun_G$ to provide alternative presentations of quasi-compact open substacks. Finally, we prove that $Bun_G$ is smooth over $S$ if $G$ is smooth and $X \to S$ is a relative curve.
representative citing papers
For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.
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Moduli stacks of quiver connections and non-Abelian Hodge theory
Moduli stacks for diagrams of λ-connections are constructed and proven algebraic when the base is a smooth projective scheme over an algebraically closed field of characteristic zero.
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Congruences of first syntomic cohomology groups
For large n, mod p^n reductions of first syntomic cohomology groups of reflexive F-gauges on O_K are isomorphic iff mod p^{2n} reductions of attached Breuil-Kisin modules with G_K-action and Nygaard filtration are isomorphic.