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2 results

  • Exact functors on perverse coherent sheaves

  • Part of
  • Clemens Koppensteiner
  • Journal:
    Compositio Mathematica / Volume 151 / Issue 9 / September 2015
    Published online by Cambridge University Press:
    04 May 2015, pp. 1688-1696
    Print publication:
    September 2015
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  • Inspired by symplectic geometry and a microlocal characterizations of perverse (constructible) sheaves we consider an alternative definition of perverse coherent sheaves. We show that a coherent sheaf is perverse if and only if $R{\rm\Gamma}_{Z}{\mathcal{F}}$ is concentrated in degree $0$ for special subvarieties $Z$ of $X$. These subvarieties $Z$ are analogs of Lagrangians in the symplectic case.

  • On the vanishing of local cohomology in characteristic p > 0

  • Gennady Lyubeznik
  • Journal:
    Compositio Mathematica / Volume 142 / Issue 1 / January 2006
    Published online by Cambridge University Press:
    13 January 2006, pp. 207-221
    Print publication:
    January 2006
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  • Let R be a d-dimensional regular local ring of characteristic p > 0 with maximal ideal $\mathfrak m$, let I be an ideal of R and let A = R/I. We describe some properties of the local cohomology module HiI(R), in particular its vanishing, in terms of the Frobenius action on the local cohomology module $H^{d-i}_{\mathfrak m}(A)$.