ar X iv : m at h / 02 10 19 4 v 1 [ m at h . G M ] 1 4 O ct 2 00 2 ALGEBRAS WITH THE SAME ( ALGEBRAIC ) GEOMETRY

ar X iv : m at h / 03 08 02 3 v 2 [ m at h . Q A ] 1 3 O ct 2 00 3 MONOMIAL HOPF ALGEBRAS

Let K be a field of characteristic 0 containing all roots of unity. We classified all the Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.

ar X iv : m at h / 02 10 19 9 v 1 [ m at h . Q A ] 1 4 O ct 2 00 2 A locally trivial quantum Hopf bundle

We describe a locally trivial quantum principal U (1)-bundle over the quantum space S 2 pq which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra (irreducible *-representations and topological K-groups) and its Galois aspects (Galois property, existence of a strong connection, non-cleftness).

ar X iv : m at h / 06 10 30 1 v 1 [ m at h . A G ] 9 O ct 2 00 6 ALGEBRAIC NAHM TRANSFORM FOR PARABOLIC HIGGS BUNDLES ON P

— In this paper, we give a completely algebraic description of Nahm transform for parabolic Higgs bundles on P. 2 KÜRŞAT AKER & SZILÁRD SZABÓ

ar X iv : m at h / 02 10 22 5 v 1 [ m at h . A G ] 1 5 O ct 2 00 2 RATIONAL CONNECTIVITY AND SECTIONS OF FAMILIES OVER CURVES TOM

ar X iv : m at h / 04 10 16 2 v 1 [ m at h . A T ] 6 O ct 2 00 4 EQUIVARIANT UNIVERSAL COEFFICIENT AND KÜNNETH SPECTRAL SEQUENCES

We construct hyper-homology spectral sequences of Z-graded and RO(G)-graded Mackey functors for Ext and Tor over G-equivariant S-algebras (A∞ ring spectra) for finite groups G. These specialize to universal coefficient and Künneth spectral sequences.