9 research outputs found
A Grothendieck-Lefschetz theorem for equivariant Picard groups
We prove a Grothendieck-Lefschetz theorem for equivariant Picard groups of
non-singular varieties with finite group actions.Comment: 7 pages; to appear in JPA
Algebraic K-theory of quotient stacks
We prove some fundamental results like localization, excision, Nisnevich
descent and the Mayer-Vietoris property for equivariant regular blow-up for the
equivariant K-theory of schemes with an affine group scheme action. We also
show that the equivariant K-theory with finite coefficients is invariant under
equivariant vector bundle morphisms. We show that the equivariant homotopy
K-theory is invariant under equivariant vector bundle morphisms and satisfies
all the above properties, including nil-invariance.Comment: 21 pages, Title changed, Final version, to appear in Annals of
K-Theor
Rigidity for equivariant pseudo pretheories
We prove versions of the Suslin and Gabber rigidity theorems in the setting
of equivariant pseudo pretheories of smooth schemes over a field with an action
of a finite group. Examples include equivariant algebraic -theory,
presheaves with equivariant transfers, equivariant Suslin homology, and Bredon
motivic cohomology.Comment: 19 pages; to appear in Journal of Algebr
Equivariant vector bundles, their derived category and -theory on affine schemes
Let be an affine group scheme over a noetherian commutative ring . We
show that every -equivariant vector bundle on an affine toric scheme over
with -action is extended from \Spec(R) for several cases of and
.
We show that given two affine schemes with group scheme actions, an
equivalence of the equivariant derived categories implies isomorphism of the
equivariant -theories as well as equivariant -theories.Comment: 34 pages, minor corrections, final version, to appear in Annals of
K-Theor
Virtual equivariant Grothendieck-Riemann-Roch formula
For a -scheme with a given equivariant perfect obstruction theory, we
prove a virtual equivariant Grothendieck-Riemann-Roch formula, this is an
extension of a result of Fantechi-G\"ottsche to the equivariant context. We
also prove a virtual non-abelian localization theorem for schemes over
with proper actions.Comment: 28 pages. Comments are welcome
Localization theorems for algebraic stacks
In this paper we consider three types of localization theorems for algebraic
stacks:
i) Concentration, or cohomological localization. Given an algebraic group
acting on a scheme or stack, we give a sufficient criterion for its localized
equivariant Borel-Moore homology to be concentrated in a given closed substack.
We deduce this from a new kind of stacky concentration theorem.
ii) Atiyah-Bott localization, or localization of (virtual) fundamental
classes to fixed loci of torus actions. In particular, this gives a conceptual
new proof of the Graber-Pandharipande formula without global embedding or
global resolution hypotheses.
iii) Cosection localization, or localization of virtual fundamental classes
to degeneracy loci of cosections (of the "obstruction sheaf"). We recast this
in terms of a notion of "cohomological reductions" of (-1)-shifted 1-forms on
derived stacks.
These results also apply to oriented Borel-Moore homology theories, such as
(higher) Chow homology and algebraic bordism, and hold over arbitrary fields
and even in mixed characteristic. In an appendix, we study various types of
fixed loci for algebraic group actions on algebraic stacks.Comment: 78 pages, comments welcom
Molecular pathogenesis and diagnostic imaging of metastatic jaw tumors
Metastasis is the spread of malignant cells from a primary tumor to distant sites through lymphatics or blood vessels. Malignant lesions metastasizing to the oral and perioral region are a rarity indeed. Malignant lesions could metastasize to both soft tissue of oral cavity and the hard tissues of the jaws and recent meta-analysis showed that metastasis is more common in the jaws than oral soft tissues because of rich vascular supply. The incidence is very low when compared to the incidence of primary oral cancers; nevertheless, one has to include in the diagnostic workup, metastatic malignant lesions, when an irregular ill-defined radiolucency or radiodensity with ragged edges in noted. It could be a challenging task for a diagnostician, in cases with the presence and location of the primary tumor is unknown. Advanced oral imaging technologies and biochemical markers play a vital role in diagnosing such lesions