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I know asking for proof-verification on MO is a tricky thing. On one hand interesting research level proofs are usually subject of articles and can not be discussed here in detail. On the other hand most simple proof which can be written on a forum are not “high-level” enough for MO and other places areRead more

Thinking about whether or not there is a natural way to transform $ L_\infty$ -algebras into $ A_\infty$ -algebras, I wonder if there is a morphism of cooperads $ \mathcal{A}ss^i\to\mathcal{L}ie^i$ from the Koszul symmetric, associative cooperad $ \mathcal{A}ss^i$ to the Koszul Lie cooperad $ \mathcal{L}ie^i$ . I think there is no such map and myRead more

Let $ C$ an irreducible, integer and proper curve over $ k$ and $ f: C \to \mathbb{P}^1$ a morphism. Let assump that one has already proved that for every closed point $ b \in \mathbb{P}^1$ there exist a unique $ c_b$ with $ c_b = f^{-1}(b)$ (so $ f$ is bijective on closed points).Read more

Let $ X$ be a proper $ k$ -scheme and $ k \subset k’$ a field extension. Consider the fibre product \ base change $ X’ = X \otimes _k k’$ . Let $ \mathcal{F} \in Coh(X)$ and $ p: X’ \to X$ the canonical projection (I think that it is a affine morphism (whyRead more