On modular p-groups

Computing Modular Invariants of p-groups

Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V ]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V ]G. We use these methods to analyse k[2V3]3 where U3 is the p-Sylow subgroup of GL3(Fp) and 2V3 i...

Separating Invariants for Modular P -groups and Groups Acting Diagonally

We study separating algebras for rings of invariants of finite groups. We describe a separating subalgebra for invariants of p-groups in characteristic p using only transfers and norms. Also we give an explicit construction of a separating set for invariants of groups acting diagonally. Let F be an algebraically closed field and let G be a finite group. Consider a faithful representation ρ : G ...

MINI-COURSE: p-MODULAR REPRESENTATIONS OF p-ADIC GROUPS

1.1. The case ` 6= p. In this case, we are in the setting of the classical Local Langlands Correspondence, which can be stated (roughly) as follows: Let n ≥ 1. We then have an injective map (1)  continuous representations of Gal(Qp/Qp) on n-dimensional Q`-vector spaces, up to isomorphism  ↪−→  irreducible, admissible representations of GLn(Qp) on Q`-vector spaces, up to isomor...

Se p 20 09 Motives for elliptic modular groups

In order to study the arithmetic structure of elliptic modular groups which are the fundamental groups of compactified modular curves with cuspidal base points, these truncated Malcev Lie algebras and their direct sums are considered as elliptic modular motives. Our main result is a new theory of Hecke operators on these motives which gives a congruence relation to the Galois action, and a moti...

Resolutions of p-Modular TQFT’s and Representations of Symmetric Groups