Let F be a totally real field, and v a place of F dividing an odd prime p. We study the weight part of Serre’s conjecture for continuous totally odd representations ρ : GF → GL2(Fp) that are reducible locally at v. Let W be the set of predicted Serre weights for the semisimplification of ρ|GFv . We prove that when ρ|GFv is generic, the Serre weights inW for which ρ is modular are exactly the on...

Let F be a totally real eld with ring of integers O and p be an odd prime unrami ed in F . Let p be a prime above p. We prove that a mod p Hilbert modular form associated to F is determined by its restriction to the partial Serre-Tate deformation space Ĝm⊗Op. Using this p-rigidity and a linear independence of mod p Hilbert modular forms restricted to the partial Serre-Tate deformation space Ĝm⊗...

General methods of investigating e ectivity on regular Hausdor (T3) spaces is considered. It is shown that there exists a functor from a category of T3 spaces into a category of domain representations. Using this functor one may look at the subcategory of e ective domain representations to get an e ectivity theory for T3 spaces. However, this approach seems to be beset by some problems. Instead...

Both intuitively, and according to similarity-based theories of induction, relevant evidence raises argument strength when it is positive and lowers it when it is negative. In three experiments, we tested the hypothesis that argument strength can actually increase when negative evidence is introduced. Two kinds of argument were compared through forced choice or sequential evaluation: single pos...

The category psBCI of pseudo-BCI-algebras and homomorphisms between them is investigated. It is also shown that the category psBCIp of p-semisimple pseudo-BCI-algebras and homomorphisms between them is a reflective subcategory of psBCI.

We study complexes of finite complete intersection dimension in the derived category of a local ring. Given such a complex of complexity c, we prove that the thick subcategory it generates contains complexes of all possible complexities at most c. In particular, we show that such a complex is virtually small, answering a question raised by Dwyer, Greenlees and Iyengar.

0. Introduction. This note announces some new methods in algebraic topology, based on the results of [1], [2] and [3]. The relative lifting problem [5, p. 415] is fundamental to that subject. It includes the extension problem, the retraction problem, the lifting problem, the section problem, the relative section problem and the computation of [X, Y] problem, among its particular cases. These pr...

Retrieving some items from memory can impair the subsequent recall of other related but not retrieved items, a phenomenon called retrieval-induced forgetting (RIF). The dominant explanation of RIF-the inhibition account-asserts that forgetting occurs because related items are suppressed during retrieval practice to reduce retrieval competition. This item inhibition persists, making it more diff...

Following Bass–Milnor–Serre, we prove that SLn(Z) has the congruence subgroup property for n ≥ 3. This was originally proved by Mennicke and Bass–Lazard–Serre. Let Γn = SLn(Z). The congruence subgroup problem for Γn (solved independently by Mennicke [Me] and Bass–Lazard–Serre [BLS]) seeks to classify all finite-index subgroups of Γn. For l ≥ 2, the level l principal congruence subgroup of Γn, d...

Let W W be a finite dimensional vector space over alttext="double-struck upper C"> <mml:mi mathvaria...