W is the category of archimedean l-groups with distinguished weak order unit, with l-group homomorphisms which preserve unit. This category includes all rings of continuous functions C(X) and all rings of measurable functions modulo null functions, with ring homomorphisms. The authors, and others, have studied previously the epimorphisms (right-cancellable morphisms) in W. There is a rich theor...

In [KLM] the authors study certain structure constants for two related rings: the spherical Hecke algebra of a split connected reductive group over a local non-Archimedean field, and the representation ring of the Langlands dual group. The former are defined relative to characteristic functions of double cosets, and the latter relative to highest weight representations. They prove that the nonv...

In the present paper, we study category-theoretic properties ofmonomorphisms in categories of log schemes. This study allows one to give a purely categorytheoretic reconstruction of the log scheme that gave rise to the category under consideration. We also obtain analogous results for categories of schemes of locally finite type over the ring of rational integers that are equipped with “archime...

Let k be a locally compact non-discrete field with non-Archimedean valuation (Say, just the p-adic numbers Qp), O its ring of integers (say Zp) and P a generator for the maximal ideal of O (i.e. p). In future lectures we will see how Hecke algebras relate to the representation theory of reductive algebraic groups over these fields. The main example to keep in mind is G = GL(n, k). When I talk a...

In pointfree topology, a continuous real function on a frame L is a map L(R) → L from the frame of reals into L. The discussion of continuous real functions with possibly infinite values can be easily brought to pointfree topology by replacing the frame L(R) with the frame of extended reals L ( R ) (i.e. the pointfree counterpart of the extended real line R = R ∪ {±∞}). One can even deal with a...

Let F be a number field with discriminant ∆F . Denote its (normalized) absolute values by SF , and write SF = Sfin · ∪ S∞, where S∞ denotes the collection of all archimedean valuations. For simplicity, we use v (resp. σ) to denote elements in Sfin (resp. S∞). Denote by A = AF the ring of adeles of F , by Glr(A) the rank r general linear group over A, and write A := Afin ⊕A∞ and GLr(A) := GLr(A)...

Throughout we let K be an algebraic number field, VK the set of all inequivalent valuations on K, and V ∞ K ⊆ VK the subset of archimedean valuations. We will use S to denote a finite subset of VK that contains V ∞ K , and we write the corresponding ring of S-integers in K as OS. In this paper, G will always be a connected non-commutative absolutely simple algebraic K-group. Any group of the fo...

Let F be a number field with discriminant ∆F . Denote its (normalized) absolute values by SF , and write SF = Sfin · ∪ S∞, where S∞ denotes the collection of all archimedean valuations. For simplicity, we use v (resp. σ) to denote elements in Sfin (resp. S∞). Denote by A = AF the ring of adeles of F , and Glr(A) the rank r general linear group over A, and write A := Afin ⊕A∞ and Glr(A) := Glr(A...

Abstract Given a commutative semiring with compatible preorder satisfying version of the Archimedean property, asymptotic spectrum, as introduced by Strassen (J. reine angew. Math. 1988), is an essentially unique compact Hausdorff space together map from to ring continuous functions. Strassen’s theorem characterizes relaxation that asymptotically compares large powers elements up subexponential...