In this paper, we study the André-Quillen homology of simplicial commutative l-algebras, l a field, having certain vanishing properties. When l has non-zero characteristic, we obtain an algebraic version of a theorem of J.-P. Serre and Y. Umeda that characterizes such simplicial algebras having bounded homotopy groups. We further discuss how this theorem fails in the rational case and, as an ap...

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...

Stimuli that capture the central tendency of presented exemplars are often preferred-a phenomenon also known as the classic beauty-in-averageness effect. However, recent studies have shown that this effect can reverse under certain conditions. We propose that a key variable for such ugliness-in-averageness effects is the category structure of the presented exemplars. When exemplars cluster into...

The non-trivial hereditary monocoreflective subcategories of the Abelian groups are the following ones: {G ∈ ObAb | G is a torsion group, and ∀g ∈ G the exponent of any prime p in the prime factorization of o(g) is at most E(p)}, where E(·) is an arbitrary function from the prime numbers to {0, 1, 2, ...,∞}. (o(·) means the order of an element, and n ≤ ∞ means n < ∞.) This result is dualized to...

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⊗...

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...

We classify all the localizing subcategories of the derived category D(R) of modules over a noetherian ring R, after developing the theory of unbounded complexes over R. Then, we use this classification to classify thick subcategories of the derived category D(R)proj of bounded complexes of projective modules over R, and prove Balmer’s reconstruction theorem in the affine case.

We describe examples motivated by the work of Serre and Abhyankar. Subject Class: Primary 11F22, 11F03. Secondary 30F35, 20C34.

Following Krause [Kra99], we prove Krull-Schmidt theorems for thick subcategories of various triangulated categories: derived categories of rings, noetherian stable homotopy categories, stable module categories over Hopf algebras, and the stable homotopy category of spectra. In all these categories, it is shown that the thick ideals of small objects decompose uniquely into indecomposable thick ...

Object recognition is one of the fundamental challenges in computer vision, where the goal is to identify and localize the extent of object instances within an image. The current de facto standard for building high-performance object category detectors is the sliding window approach. This approach involves scanning an image with a fixed-size rectangular window and applying a classifier to the f...