Results 11  20
of
395
Compact moduli of plane curves
, 2004
"... We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C ⊂ P 2 as a surfacedivisor pair (P 2, C) and define Md as a moduli space of pairs (X, D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack Md is smo ..."
Abstract

Cited by 28 (6 self)
 Add to MetaCart
We construct a compactification Md of the moduli space of plane curves of degree d. We regard a plane curve C ⊂ P 2 as a surfacedivisor pair (P 2, C) and define Md as a moduli space of pairs (X, D) where X is a degeneration of the plane. We show that, if d is not divisible by 3, the stack Md is smooth and the degenerate surfaces X can be described explicitly.
Smashing Subcategories And The Telescope Conjecture  An Algebraic Approach
 Invent. Math
, 1998
"... . We prove a modified version of Ravenel's telescope conjecture. It is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite spectra. This result is based on a new characterization of smashing subcategories, which leads in addition to a cl ..."
Abstract

Cited by 25 (6 self)
 Add to MetaCart
. We prove a modified version of Ravenel's telescope conjecture. It is shown that every smashing subcategory of the stable homotopy category is generated by a set of maps between finite spectra. This result is based on a new characterization of smashing subcategories, which leads in addition to a classification of these subcategories in terms of the category of finite spectra. The approach presented here is purely algebraic; it is based on an analysis of pureinjective objects in a compactly generated triangulated category, and covers therefore also situations arising in algebraic geometry and representation theory. Introduction Smashing subcategories naturally arise in the stable homotopy category S from localization functors l : S ! S which induce for every spectrum X a natural isomorphism l(X) ' X l(S) between the localization of X and the smash product of X with the localization of the sphere spectrum S. In fact, a localization functor has this property if and only if it preserv...
Formalized mathematics
 TURKU CENTRE FOR COMPUTER SCIENCE
, 1996
"... It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In c ..."
Abstract

Cited by 23 (0 self)
 Add to MetaCart
It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In contrast to the QED Manifesto however, we do not offer polemics in support of such a project. We merely try to place the formalization of mathematics in its historical perspective, as well as looking at existing praxis and identifying what we regard as the most interesting issues, theoretical and practical.
A Bost–Connes–Marcolli system for Shimura varieties, in preparation
"... We construct a Quantum Statistical Mechanical system (A, σt) analogous to the BostConnesMarcolli system of [CM04] in the case of Shimura varieties. Along the way, we define a new BostConnes system for number fields which has the “correct” symmetries and the “correct ” partition function. We give ..."
Abstract

Cited by 21 (0 self)
 Add to MetaCart
We construct a Quantum Statistical Mechanical system (A, σt) analogous to the BostConnesMarcolli system of [CM04] in the case of Shimura varieties. Along the way, we define a new BostConnes system for number fields which has the “correct” symmetries and the “correct ” partition function. We give a formalism that applies to general Shimura data (G, X). The object of this series of papers is to show that these systems have phase transitions and spontaneous symmetry breaking, and to classify their KMS states, at least for low temperature.
Cyclic Cohomology of Étale Groupoids; The General Case
 Ktheory
, 1999
"... We give a general method for computing the cyclic cohomology of crossed products by 'etale groupoids, extending the FeiginTsyganNistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor and Tsygan for the convolution alge ..."
Abstract

Cited by 21 (1 self)
 Add to MetaCart
We give a general method for computing the cyclic cohomology of crossed products by 'etale groupoids, extending the FeiginTsyganNistor spectral sequences. In particular we extend the computations performed by Brylinski, Burghelea, Connes, Feigin, Karoubi, Nistor and Tsygan for the convolution algebra C 1 c (G) of an 'etale groupoid, removing the Hausdorffness condition and including the computation of hyperbolic components. Examples like group actions on manifolds and foliations are considered. Keywords: cyclic cohomology, groupoids, crossed products, duality, foliations. Contents 1 Introduction 3 2 Homology and Cohomology of Sheaves on ' Etale Groupoids 4 2.1 ' Etale Groupoids : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 4 2.2 \Gamma c in the nonHausdorff case : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.3 Homology and Cohomology of ' Etale Groupoids : : : : : : : : : : : : : : : : : : : : : 8 3 Cyclic Homologies of Sheaves ...