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2-Cohomology of semi-simple simply connected group-schemes over curves defined over p -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

Let X be a proper, smooth, geometrically connected curve over a p -adic field k . Lichtenbaum proved that there exists a perfect duality: Br ( X ) × Pic ( X ) / between the Brauer and the Picard group of X , from which he deduced the existence of an injection of Br ( X ) in P X Br ( k P ) where P X and k P denotes the residual field of the point P . The aim of this paper is to prove that if G = G ˜ is an X e t - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results the neutrality of every X e t -gerb which...

A categorical quotient in the category of dense constructible subsets

Devrim Celik (2009)

Colloquium Mathematicae

A. A'Campo-Neuen and J. Hausen gave an example of an algebraic torus action on an open subset of the affine four space that admits no quotient in the category of algebraic varieties. We show that this example admits a quotient in the category of dense constructible subsets and thereby answer a question of A. Białynicki-Birula.

A combinatorial construction of sets with good quotients by an action of a reductive group

Joanna Święcicka (2001)

Colloquium Mathematicae

The aim of this paper is to construct open sets with good quotients by an action of a reductive group starting with a given family of sets with good quotients. In particular, in the case of a smooth projective variety X with Pic(X) = 𝒵, we show that all open sets with good quotients that embed in a toric variety can be obtained from the family of open sets with projective good quotients. Our method applies in particular to the case of Grassmannians.

A dimension formula for Ekedahl-Oort strata

Ben Moonen (2004)

Annales de l’institut Fourier

We study the Ekedahl-Oort stratification on moduli spaces of PEL type. The strata are indexed by the classes in a Weyl group modulo a subgroup, and each class has a distinguished representative of minimal length. The main result of this paper is that the dimension of a stratum equals the length of the corresponding Weyl group element. We also discuss some explicit examples.

A duality theorem for Dieudonné displays

Eike Lau (2009)

Annales scientifiques de l'École Normale Supérieure

We show that the Zink equivalence between p -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic p is compatible with duality. The proof relies on a new explicit formula for the p -divisible group associated to a Dieudonné display.

A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula

Kai Köhler, Damien Roessler (2002)

Annales de l’institut Fourier

This is the second of a series of papers dealing with an analog in Arakelov geometry of the holomorphic Lefschetz fixed point formula. We use the main result of the first paper to prove a residue formula "à la Bott" for arithmetic characteristic classes living on arithmetic varieties acted upon by a diagonalisable torus; recent results of Bismut- Goette on the equivariant (Ray-Singer) analytic torsion play a key role in the proof.

A general Hilbert-Mumford criterion

Jürgen Hausen (2003)

Annales de l’institut Fourier

Let a reductive group G act on an algebraic variety X . We give a Hilbert-Mumford type criterion for the construction of open G -invariant subsets V X admitting a good quotient by G .

A genericity theorem for algebraic stacks and essential dimension of hypersurfaces

Zinovy Reichstein, Angelo Vistoli (2013)

Journal of the European Mathematical Society

We compute the essential dimension of the functors Forms n , d and Hypersurf n , d of equivalence classes of homogeneous polynomials in n variables and hypersurfaces in n 1 , respectively, over any base field k of characteristic 0 . Here two polynomials (or hypersurfaces) over K are considered equivalent if they are related by a linear change of coordinates with coefficients in K . Our proof is based on a new Genericity Theorem for algebraic stacks, which is of independent interest. As another application of the...

A geometric algorithm for the output functional controllability in general manipulation systems and mechanisms

Paolo Mercorelli (2012)


In this paper the control of robotic manipulation is investigated. Manipulation system analysis and control are approached in a general framework. The geometric aspect of manipulation system dynamics is strongly emphasized by using the well developed techniques of geometric multivariable control theory. The focus is on the (functional) control of the crucial outputs in robotic manipulation, namely the reachable internal forces and the rigid-body object motions. A geometric control procedure is outlined...

A geometric procedure for robust decoupling control of contact forces in robotic manipulation

Paolo Mercorelli, Domenico Prattichizzo (2003)


This paper deals with the problem of controlling contact forces in robotic manipulators with general kinematics. The main focus is on control of grasping contact forces exerted on the manipulated object. A visco-elastic model for contacts is adopted. The robustness of the decoupling controller with respect to the uncertainties affecting system parameters is investigated. Sufficient conditions for the invariance of decoupling action under perturbations on the contact stiffness and damping parameters...

A Geometrical Construction for the Polynomial Invariants of some Reflection Groups

Sarti, Alessandra (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 20F55, 13F20; Secondary 14L30.We construct invariant polynomials for the reflection groups [3, 4, 3] and [3, 3, 5] by using some special sets of lines on the quadric P1 × P1 in P3. Then we give a simple proof of the well known fact that the ring of invariants are rationally generated in degree 2,6,8,12 and 2,12,20,30.

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