### A bound for the torsion in the $K$-theory of algebraic integers.

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We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.

This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension $\le 4$ and $\ge 11$. Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real quadrics....

On montre que si la conjecture de Farrell-Jones en $K$-théorie algébrique est vérifiée alors celle de la $K$-théorie hermitienne est équivalente à l’existence d’un entier $p\in Z$ tel que “assembly map” soit un isomorphisme en degré $p$ et $p+1$.

One defines a Riemann-Roch natural transformation from algebraic to topological higher bivariant K-theory in the category of complex spaces.

It was recently proved that every additive category has a unique maximal exact structure, while it remained open whether the distinguished short exact sequences of this canonical exact structure coincide with the stable short exact sequences. The question is answered by a counterexample which shows that none of the steps to construct the maximal exact structure can be dropped.