A Gersten–Witt spectral sequence for regular schemes
A purity theorem for the Witt group
Algebraic K-Theory and Quadratic Forms.
Algebraic properties of decorated splitting obstruction groups
In questo articolo si riassumono le definizioni e le principali proprietà dei gruppi di ostruzione con decorazione di tipo LS e LP. Si stabiliscono nuove relazioni fra questi gruppi e si descrivono le proprietà delle mappe naturali fra differenti gruppi con decorazione. Si costruiscono varie successioni spettrali, contenenti questi gruppi con decorazione, e si studiano la loro connessione con le successioni spettrali in -teoria per certe estensioni quadratiche di antistrutture. Infine, si introduce...
Dualization in algebraic K-theory and the invariant e¹ of quadratic forms over schemes
In the classical Witt theory over a field F, the study of quadratic forms begins with two simple invariants: the dimension of a form modulo 2, called the dimension index and denoted e⁰: W(F) → ℤ/2, and the discriminant e¹ with values in k₁(F) = F*/F*², which behaves well on the fundamental ideal I(F)= ker(e⁰). Here a more sophisticated situation is considered, of quadratic forms over a scheme and, more generally, over an exact category with duality. Our purposes are: ...
Function Fields of Quadratic Forms.
Geometric description of the connecting homomorphism for Witt groups.
Homology stability for the special linear group of a field and Milnor-Witt -theory.
Homology stability for unitary groups.
- and -theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by .
Lie perfect, Lie central extension and generalization of nilpotency in multiplicative Lie algebras
This paper aims to introduce and explore the concept of Lie perfect multiplicative Lie algebras, with a particular focus on their connections to the central extension theory of multiplicative Lie algebras. The primary objective is to establish and provide proof for a range of results derived from Lie perfect multiplicative Lie algebras. Furthermore, the study extends the notion of Lie nilpotency by introducing and examining the concept of local nilpotency within multiplicative Lie algebras. The...
L-theory and dihedral homology.
Natural homomorphisms of Witt rings of orders in algebraic number fields. II
We prove that there are infinitely many real quadratic number fields with the property that for infinitely many orders in and for the maximal order in the natural homomorphism of Witt rings is surjective.
Natural homomorphisms of Witt rings of orders in algebraic number fields
On -equivariant homology.
On the domain of the assembly map in algebraic -theory.
On the Witt rings of function fields of quasihomogeneous varieties
Picard groups of Witt rings.
Relation entre les conjectures de Farrell-Jones en -théories algébrique et hermitienne
On montre que si la conjecture de Farrell-Jones en -théorie algébrique est vérifiée alors celle de la -théorie hermitienne est équivalente à l’existence d’un entier tel que “assembly map” soit un isomorphisme en degré et .
Rigidity II: non-orientable case.