N ov 2 00 5 Cohomology of F 1 - schemes Anton

2 00 7 Homological algebra over belian categories and cohomology of F 1 - schemes Anton Deitmar

1 Belian categories 2 1.1 Complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Pull-backs and push-outs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Ascent functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.4 Snake Lemma . . . . . . . . . . . . . . . . . . . . . ....

ov 2 00 8 Higher order invariants , cohomology , and automorphic forms Anton

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and ...

7 N ov 2 00 8 Higher order invariants , cohomology , and automorphic forms

A general structure theorem on higher order invariants is proven. For an arithmetic group, the structure of the corresponding Hecke module is determined. It is shown that the module does not contain any irreducible submodule. This explains the fact that L-functions of higher order forms have no Euler-product. Higher order cohomology is introduced, classical results of Borel are generalized and ...

m at h . A G ] 5 N ov 2 00 1 HILBERT SCHEMES AND W ALGEBRAS

We construct geometrically a W algebra which acts irreducibly on the direct sum of the cohomology rings of the Hilbert schemes X [n] of n points on a projective surface X for all n ≥ 0. We compute explicitly the commutators among a set of linear basis elements of the W algebra, and identify this algebra with a W1+∞-type algebra. A precise formula of certain Chern character operators, which is e...

N ov 2 00 1 Cohomology of Restricted Lie Algebras