25 research outputs found
On the vanishing of negative K-groups
Let k be an infinite perfect field of positive characteristic p and assume
that strong resolution of singularities holds over k. We prove that, if X is a
d-dimensional noetherian scheme whose underlying reduced scheme is essentially
of finite type over the field k, then the negative K-group K_q(X) vanishes for
every q < -d. This partially affirms a conjecture of Weibel.Comment: Math. Ann. (to appear
On the curvature of vortex moduli spaces
We use algebraic topology to investigate local curvature properties of the
moduli spaces of gauged vortices on a closed Riemann surface. After computing
the homotopy type of the universal cover of the moduli spaces (which are
symmetric powers of the surface), we prove that, for genus g>1, the holomorphic
bisectional curvature of the vortex metrics cannot always be nonnegative in the
multivortex case, and this property extends to all Kaehler metrics on certain
symmetric powers. Our result rules out an established and natural conjecture on
the geometry of the moduli spaces.Comment: 25 pages; final version, to appear in Math.
On the existence of a compact generator on the derived category of a noetherian formal scheme
In this paper, we prove that for a noetherian formal scheme X, its derived
category of sheaves of modules with quasi-coherent torsion homologies D_qct(X)
is generated by a single compact object. In an appendix we prove that the
category of compact objects in D_qct(X) is skeletally small.Comment: 13 page