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The main purpose of this paper is to make Nakayamas theorem more accessible. We give a proof of Nakayamas theorem based on the negative definiteness of intersection matrices of exceptional curves. In this paper, we treat Nakayamas theorem on algebraic varieties over any algebraically closed field of arbitrary characteristic although Nakayamas original statement is formulated for complex analytic spaces.
We give a new proof of Bradens theorem ([Br]) about emph{hyperbolic restrictions} of constructible sheaves/D-modules. The main geometric ingredient in the proof is a 1-parameter family that degenerates a given scheme Z equipped with a G_m-action to the product of the attractor and repeller loci.
For a proper semistable curve $X$ over a DVR of mixed characteristics we reprove the invariant cycles theorem with trivial coefficients (see Chiarellotto, 1999) i.e. that the group of elements annihilated by the monodromy operator on the first de Rha
Let G be the Tate module of a p-divisble group H over a perfect field k of characteristic p. A theorem of Scholze-Weinstein describes G (and therefore H itself) in terms of the Dieudonne module of H; more precisely, it describes G(C) for good semiper
In this paper, we show Langtons type theorem on separatedness and properness of moduli functor of torsion free semistable sheaves on algebraic orbifolds over an algebraically closed field k
In this note I provide two extensions of a particular case of the classical Poncelet theorem.