The Classification of Thick Subcategories and Balmer’s Reconstruction Theorem

نویسنده

  • TAKUMI MURAYAMA
چکیده

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.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Classifying Thick Subcategories of the Stable Category of Cohen-macaulay Modules

Various classification theorems of thick subcategories of a triangulated category have been obtained in many areas of mathematics. In this paper, as a higher dimensional version of the classification theorem of thick subcategories of the stable category of finitely generated representations of a finite p-group due to Benson, Carlson and Rickard, we consider classifying thick subcategories of th...

متن کامل

Thick Subcategories in Stable Homotopy Theory 3

In this series of lectures we give an exposition of the seminal work of Devinatz, Hopkins, and Smith which is surrounding the classification of the thick subcategories of finite spectra in stable homotopy theory. The lectures are expository and are aimed primarily at non-homotopy theorists. We begin with an introduction to the stable homotopy category of spectra, and then talk about the celebra...

متن کامل

Stratifying Modular Representations of Finite Groups

We classify localising subcategories of the stable module category of a finite group that are closed under tensor product with simple (or, equivalently all) modules. One application is a proof of the telescope conjecture in this context. Others include new proofs of the tensor product theorem and of the classification of thick subcategories of the finitely generated modules which avoid the use ...

متن کامل

Ascent of Finiteness of Flat Dimension

The main focus of this talk is to prove ascent of finiteness of flat dimension through local homomorphisms. Descent is known classically, e.g., it is in Cartan–Eilenberg’s book on homological algebra, but the corresponding ascent property is surprising because of the need to use derived categories. We present a short proof of ascent due to Dwyer–Greenlees–Iyengar, and discuss the main ingredien...

متن کامل

Classifying thick subcategories of perfect complexes

Given a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes Dper(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of (iso-classes for) indecomposable injective modules are essentially used.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2015