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Can anyone provide a reference for the Kodaira-Spencer map in the logarithmic geometry setting?

Let $X=\operatorname{Spec} A$ be an affine variety. Consider the log structure given by $\mathbb N\rightarrow A$ which sends $1\mapsto 0$. Also consider the log structure $\mathbb N^r \rightarrow A$ g …

Let $G$ be a reductive group. A $2$-shifted $2$-form on the classifying stack $BG$ is by definition a a morphism of quasi-coherent complexes \begin{equation} \mathcal O_{BG}\rightarrow (\wedge^2 \math …

Let $X$ be a smooth complex analytic manifold and $D$ be a normal crossing divisor. Suppose that there is a complex analytic logarithmic symplectic structure on $X$. Is there a Darboux like theorem th …

I have two questions on logarithmic schemes Can we explicitly construct a chart for any coherent logarithmic scheme? By definition of coherence it must have a chart but given a coherent sheaf of mon …

Suppose we have a commutative diagram of Artin stacks $ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\p …

This is a question related to Semistable curves of genus $g\geq 2$ form an Artin algebraic stack in the etale topology? Let $\mathcal C\rightarrow \mathcal M^{ss}_g$ be the universal curve over the A …

Let $A_{\bullet}$ and $B_{\bullet}$ be two bounded complexes of sheaves over a variety $X$. Is there a Kunneth-like formula for the hypercohomology of the tensor product $A_{\bullet}\otimes B_{\bullet …

There are two ways to define a stack. The first one is that the presheaf of sets Isom (a,b) is a sheaf and that every descent data is effective. The second one says that a stack is a homotopy sheaf of …