Packets in Grothendieck's Section Conjecture

Using the identification of sections of the Galois group of the ground field into the arithmetic fundamental group with neutral fiber functors of the category of finite connections, we define the "packets" in Grothendieck's section conjecture and show their properties predicted by him.Comment: 22 pages (no changes on the mathematical content but the exposition has been shortened

Unoriented geometric functors

Farrell and Hsiang noticed that the geometric surgery groups defined By Wall, Chapter 9, do not have the naturality Wall claims for them. They were able to fix the problem by augmenting Wall's definitions to keep track of a line bundle. The definition of geometric Wall groups involves homology with local coefficients and these also lack Wall's claimed naturality. One would hope that a geometric bordism theory involving non-orientable manifolds would enjoy the same naturality as that enjoyed by homology with local coefficients. A setting for this naturality entirely in terms of local coefficients is presented in this paper. Applying this theory to the example of non-orientable Wall groups restores much of the elegance of Wall's original approach. Furthermore, a geometric determination of the map induced by conjugation by a group element is given.Comment: 12 pages, LaTe

Canonical bases and affine Hecke algebras of type D

We prove a conjecture of Kashiwara and Miemietz on canonical bases and branching rules of affine Hecke algebras of type D. The proof is similar to the proof of the type B case.Comment: 24 page

Simplicial Differential Calculus, Divided Differences, and Construction of Weil Functors

We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules over a topological ring K. This calculus has the advantage that the number of evaluation points growths linearly with the degree, and not exponentially as in the classical, "cubic" approach. In particular, it is better adapted to the case of positive characteristic, where it permits to define Weil functors corresponding to scalar extension from K to truncated polynomial rings K[X]/(X^{k+1}).Comment: V2: minor changes, and chapter 3: new results included; to appear in Forum Mathematicu