1)(2j − 1) complex coefficients (see[1]). Hence the space C/ ∼ (where two points are equivalent if the corresponding polynomials define isomorphic bundles) parametrizes isomorphism classes of bundles on the blown-up plane with splitting O(j) ⊕ O(−j) over the exceptional divisor. Denote the set of these isomorphism classes by Mj and give C / ∼ the quotient topology. We have just shown that there...

In the case that K is a number field, this conjecture goes back almost thirty years. The Lie algebra analogue has been formulated by J. Tate [18], D. Mumford [10], and J.-P. Serre [13]. A more precise conjecture involves comparison with the singular homology group H1(A(C),Q) for a fixed embedding K ⊂ C. If G∞ denotes the associated Hodge group (cf. §4), the “Mumford-Tate” conjecture states that...

We provide a complete classification of the class unital graph $C^*$-algebras - prominently containing full family Cuntz-Krieger algebras showing that Morita equivalence in this case is determined by ordered, filtered $K$-theory. The result geometric sense it establishes any between $C^*(E)$ and $C^*(F)$ can be realized sequence moves leading from $E$ to $F$, way resembling role Reidemeister on...

We prove an equivariant analogue of Chevalley’s isomorphism theorem for polynomial, C∞ or Cω maps.

we define a new function-valued inner product on l2(g), called ?-bracket product, where g is a locally compact abelian group and ? is a topological isomorphism on g. we investigate the notion of ?-orthogonality, bessel's inequality and ?-orthonormal bases with respect to this inner product on l2(g).

(a) isomorphism ∼=, elementary equivalence ≡, elementary equivalence ≡α for Lω1,ω sentences of rank < α. (b) Isomorphism of countable graphs, linear orders, countable Boolean algebras is ≤B complete for orbit equivalence relations of continuous S∞ actions (≤B is Borel reducibility, S∞ is the Polish group of permutations of ω). (c) for ∼= is partially answered in computable model theory, with no...