On the group .
On the index of nonlocal elliptic operators for compact Lie groups
We consider a class of nonlocal operators associated with a compact Lie group G acting on a smooth manifold. A notion of symbol of such operators is introduced and an index formula for elliptic elements is obtained. The symbol in this situation is an element of a noncommutative algebra (crossed product by G) and to obtain an index formula, we define the Chern character for this algebra in the framework of noncommutative geometry.
On the K-theory of the -algebra generated by the left regular representation of an Ore semigroup
We compute the -theory of -algebras generated by the left regular representation of left Ore semigroups satisfying certain regularity conditions. Our result describes the -theory of these semigroup -algebras in terms of the -theory for the reduced group -algebras of certain groups which are typically easier to handle. Then we apply our result to specific semigroups from algebraic number theory.
On the leading terms of zeta isomorphisms and -adic -functions in non-commutative Iwasawa theory.
On the Milnor -groups of complete discrete valuation fields.
On the multiplicative independence of binomial coefficients
On the nonexistence of certain morphisms from Grassmannian to Grassmannian in characteristic 0.
On the non-torsion elements in the algebraic K-theory of rings of integers.
On the odd part of tame kernels of biquadratic number fields
On the corresponding to bialgebras
On the p-rank of the tame kernel of algebraic number fields.
On the real cohomology of arithmetic groups and the rank conjecture for number fields
On the real cohomology of spaces of free loops on manifolds
Let LX be the space of free loops on a simply connected manifold X. When the real cohomology of X is a tensor product of algebras generated by a single element, we determine the algebra structure of the real cohomology of LX by using the cyclic bar complex of the de Rham complex Ω(X) of X. In consequence, the algebra generators of the real cohomology of LX can be represented by differential forms on LX through Chen’s iterated integral map. Let be the circle group. The -equivariant cohomology...
On the structure of Milnor -groups of certain complete discrete valuation fields
For a typical example of a complete discrete valuation field of type II in the sense of [12], we determine the graded quotients for all . In the Appendix, we describe the Milnor -groups of a certain local ring by using differential modules, which are related to the theory of syntomic cohomology.
On the universal -algebra generated by a partial isometry.
On the values of equivariant zeta functions of curves over finite fields.
On the Witt rings of function fields of quasihomogeneous varieties
On the zeta function of a complete intersection
On two-primary algebraic K-theory of quadratic number rings with focus on K₂
On -rings and topological realization.