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Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.

1 vote
1 answer
254 views

About the canonical morphism from $f^{*}f_{*}f^{*}F$ to $f^{*}F$

Assume $X$ and $Y$ are noetherian schemes over $\mathbb{C}$ and there is a proper and faithfully flat morphism $f: X\rightarrow Y$. Assume the canonical morphism $F\xrightarrow{\sim} f_{*}f^{*}F$ is …
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4 votes
0 answers
330 views

Modules over an Azumaya algebra and modules over the associated Brauer-Severi variety

Assume $\mathcal{A}$ is an Azumaya algebra of rank $r^2$ on a smooth projective scheme $Y$ over $\mathbb{C}$. Let $f: X\rightarrow Y$ be the Brauer-Severi variety associated to $\mathcal{A}$. I read …
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