Algebraic groups with a distinguished conjugacy class.
Algebraic -theory and crystalline cohomology
Algebraic leaves of algebraic foliations over number fields
We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field embedded in , a smooth algebraic variety over , equipped with a rational point , and an algebraic subbundle of the its tangent bundle , defined over . Assume moreover that the vector bundle is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold , and one may consider its leaf through . We prove...
Algebraic Legendrian varieties [Book]
Algebraic loop groups and moduli spaces of bundles
We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.
Algebraic methods in the theory of theta functions
Algebraic SL(2)-actions: deformations of infinite isotropy subgroups
Algebraic tori as Nisnevich sheaves with transfers
We relate -equivalence on tori with Voevodsky’s theory of homotopy invariant Nisnevich sheaves with transfers and effective motivic complexes.
Algebraic zip data.
Algebras with finitely generated invariant subalgebras
We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.
Algèbres de groupe du groupe additif
Almost proper GIT-stacks and discriminant avoidance.
An analytic construction of degenerating abelian varieties over complete rings
An elementary proof of the Hilbert-Mumford criterion.
An Equivariant Lefschetz Formula for Finite Reductive Groups.
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
An explicit formula for the Hilbert symbol of a formal group
A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ()-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ()-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas for the...
An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation do not...
An orbit closure for a representation of the Kronecker quiver with bad singularities
We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
Analytic curves in power series rings