Corrigendum: Connected components of affine Deligne–Lusztig varieties in mixed characteristic

Connected Components of Affine Deligne-lusztig Varieties in Mixed Characteristic

We determine the set of connected components of minuscule affine Deligne-Lusztig varieties for special maximal compact subgroups of unramified connected reductive groups. Partial results are also obtained for non-minuscule closed affine Deligne-Lusztig varieties. We consider both the function field case and its analog in mixed characteristic. In particular, we determine the set of connected com...

Connected Components of Closed Affine Deligne-lusztig Varieties

We determine the set of connected components of closed affine Deligne-Lusztig varieties for special maximal compact subgroups of split connected reductive groups. We show that there is a transitive group action on this set. Thus such an affine Deligne-Lusztig variety has isolated points if and only if its dimension is 0. We also obtain a description of the set of these varieties that are zero-d...

Irreducible components of characteristic varieties

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial di.erential equations de0ned from a suitable 0ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety de0ned from the order 0ltration is involutive. More explicitly, we consider a 0ltration of An induced by any vector (u...

Models of Shimura varieties in mixed characteristic

On Unramified Morphisms of Affine Varieties into Simply Connected Non-singular Affine Varieties

The Jacobian Conjecture is the following : If φ ∈ Endk(Ank ) with a field k of characteristic zero is unramified, then φ is an automorphism. In this paper, This conjecture is proved affirmatively in the abstract way instead of treating variables in a polynomial ring. Let k be an algebraically closed field, let Ak = Max(k[X1, . . . , Xn]) be an affine space of dimension n over k and let f : Ak −...