1,898 research outputs found
Foliations and webs inducing Galois coverings
We introduce the notion of Galois holomorphic foliation on the complex
projective space as that of foliations whose Gauss map is a Galois covering
when restricted to an appropriate Zariski open subset. First, we establish
general criteria assuring that a rational map between projective manifolds of
the same dimension defines a Galois covering. Then, these criteria are used to
give a geometric characterization of Galois foliations in terms of their
inflection divisor and their singularities. We also characterize Galois
foliations on admitting continuous symmetries, obtaining a
complete classification of Galois homogeneous foliations
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
Tame class field theory for arithmetic schemes
We extend the unramified class field theory for arithmetic schemes of K. Kato
and S. Saito to the tame case. Let be a regular proper arithmetic scheme
and let be a divisor on whose vertical irreducible components are
normal schemes.
Theorem: There exists a natural reciprocity isomorphism \rec_{X,D}:
\CH_0(X,D) \liso \tilde \pi_1^t(X,D)^\ab\. Both groups are finite.
This paper corrects and generalizes my paper "Relative K-theory and class
field theory for arithmetic surfaces" (math.NT/0204330
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