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Let $X$ be a scheme and $U$ be an open subscheme. The proof of the Thomason-Trobaugh Theorem implies that under some mild assumptions, for any perfect complex $F$ on $U$, we have that $F\oplus F[1]$ c …

It is known that if you have a reductive group acting on a regular algebra, then the ring of invariants is Cohen-Macaulay. Is this still true for Gorenstein algebras?

Is there a good introduction to characteristic cycle of D modules(or constructive sheaves)? I just encountered this concept recently and I really would like to see some examples of calculations using …

Recently I'm reading about the construction of automorphic sheaves for GLn, and I would like to see how to determine the characteristic variety of Laumon's sheaf, since it carries some information abo …

There are different descriptions of the category $Coh(\mathbf{P}^{n})$. One can either describe it as modules over Beilinson's quiver algebra (Let us denote it by $A$) using the exceptional collection …

It is well known that a picard stack on a site is equivalent to a two term complex of sheaves of abelian groups. Can we describe the isomorphism classes of gerbes of the picard stack using the tw …

Is there any known explicit description about the Fourier-Mukai transform of the theta divisor(or powers of theta divisor) on the jacobian of a smooth curve?

Take a look at FGA or the stacks project