Consider the abelian category Ck of commutative group schemes of finite type over a field k. By results of Serre and Oort, Ck has homological dimension 1 (resp. 2) if k is algebraically closed of characteristic 0 (resp. positive). In this article, we explore the abelian category of commutative algebraic groups up to isogeny, defined as the quotient of Ck by the full subcategory Fk of finite k-g...

We consider the Kudla-Millson lift from elliptic modular forms of weight (p + q)/2 to closed q-forms on locally symmetric spaces corresponding to the orthogonal group O(p, q). We study the L-norm of the lift following the Rallis inner product formula. We compute the contribution at the Archimedian place. For locally symmetric spaces associated to even unimodular lattices, we obtain an explicit ...

Let A and B be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence α between A and B such that α is induced by exact functors. We present a nice correspondence between indecomposable modules over A and B. As a consequence, we have the following: (1) If A is a self-injective algebra, then so is B; (2) If A and B are finite dimensional algebras over an algeb...

In mathematics curves are defined as the images of continuous real functions defined on closed intervals and these continuous functions are called parameterizations of the corresponding curves. If only simple curves of finite lengths are considered, then parameterizations can be restricted to the injective continuous functions or even to the continuous length-normalized parameterizations. In ad...

Let g be the isotropic Gaussian: •The representation distinguishes oriented point-sets: ψ· is injective from (R × Sd−1)∗ into L2(Rd). • It provides continuation of the normal field: ∇θψ is defined a.e. with isolated (possible) singularities near Voronoi boundaries. • It provides approximately linear composition: Given oriented point-sets S, T , ψS∪T ≈ ψS + ψT . •Given two oriented points satisf...

This paper consists of three results on Frobenius categories: (1)we give sufficient conditions on when a factor category of a Frobenius category is still a Frobenius category; (2) we show that any Frobenius category is equivalent to an extension-closed exact subcategory of the Frobenius category formed by Cohen–Macaulaymodules over some additive category; this is an analogue of Gabriel–Quillen’...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

This paper looks at a class of closed orientable 3-manifolds constructed from a gluing of three handlebodies, such that the inclusion of each handlebody is π1-injective. This construction is the generalisation to handlebodies of the condition for gluing three solid tori to produce non-Haken Seifert fibered 3-manifolds with infinite fundamental group. It is shown that there is an efficient algor...

Let S be a closed orientable surface of genus at least two, and let C be an arbitrary (complex) projective structure on S. We show that there is a decomposition of S into pairs of pants and cylinders such that the restriction of C to each component has an injective developing map and a discrete and faithful holonomy representation. This decomposition implies that every projective structure can ...

Let R be a ring and let M be a right R-module with S End MR . M is called almost general quasiprincipally injective or AGQP-injective for short if, for any 0/ s ∈ S, there exist a positive integer n and a left ideal Xsn of S such that s / 0 and lS Ker s Ss ⊕ Xsn . Some characterizations and properties of AGQP-injective modules are given, and some properties of AGQP-injective modules with additi...