Applications of weight-two motivic cohomology.
Approche de la conjecture de Novikov par la cohomologie cyclique
Area preserving pl homeomorphisms and relations in
To any compactly supported, area preserving, piecewise linear homeomorphism of the plane is associated a relation in of the smallest field whose elements are needed to write the homeomorphism.Using a formula of J. Morita, we show how to calculate the relation, in some simple cases. As applications, a “reciprocity” formula for a pair of triangles in the plane, and some explicit elements of torsion in of certain function fields are found.
Arithmetic infinite Grassmannians and the induced central extensions.
Asymptotic behaviour of numerical invariants of algebraic varieties
We show that if the degree of a nonsingular projective variety is high enough, maximization of any of the most important numerical invariants, such as class, Betti number, and any of the Chern or middle Hodge numbers, leads to the same class of extremal varieties. Moreover, asymptotically (say, for varieties whose total Betti number is big enough) the ratio of any two of these invariants tends to a well-defined constant.
Atiyahova-Singerova věta o indexu
Augmented Γ-spaces, the stable rank filtration, and a bu analogue of the Whitehead conjecture
We explore connections between our previous paper [J. Reine Angew. Math. 604 (2007)], where we constructed spectra that interpolate between bu and Hℤ, and earlier work of Kuhn and Priddy on the Whitehead conjecture and of Rognes on the stable rank filtration in algebraic K-theory. We construct a "chain complex of spectra" that is a bu analogue of an auxiliary complex used by Kuhn-Priddy; we conjecture that this chain complex is "exact"; and we give some supporting evidence. We tie this to work of...
Automorphism group of representation ring of the weak Hopf algebra
Let be the unique noncommutative and noncocommutative eight dimensional semi-simple Hopf algebra. We first construct a weak Hopf algebra based on , then we investigate the structure of the representation ring of . Finally, we prove that the automorphism group of is just isomorphic to , where is the dihedral group with order 12.
Automorphisms of Witt rings of global fields
We construct an uncountable set of strong automorphisms of the Witt ring of a global field.