A Gersten–Witt spectral sequence for regular schemes
A Pieri-Chevalley formula in the K-theory of a -bundle.
A splitting principle and the algebraic K-theory of some homogeneous varieties
Das Adams-Riemann-Roch-Theorem in der höheren äquivarianten K-Theorie.
Descent, motives and K-theory.
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: ...
Finiteness of cominuscule quantum -theory
The product of two Schubert classes in the quantum -theory ring of a homogeneous space is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on . We show that if is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to that take the marked points to general Schubert varieties and whose domains...
Gersten's conjecture for some complexes of vanishing cycles.
Helices on some Fano threefolds : constructivity of semiorthogonal bases of
of Fermat curves with divisorial support at infinity
-theory of log-schemes. I.
Les K-groupes d'un schéma éclaté et une formule d'intersection excédentaire.
Motivic Landweber exactness.
On extensions of mixed motives.
In this article we give an introduction to mixed motives and sketch a couple of ways to construct examples.
Riemann-Roch type theorems for arithmetic schemes with a finite group action.
Slices and transfers.
The connection between the -theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel
The existence of higher logarithms
The Leibniz rule in algebraic -theory.
The spectral sequence relating algebraic K-theory to motivic cohomology