To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure email@example.com
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov’s well-known characteristic-zero results, we construct dual exceptional collections on them (which are, however, not strong) as well as a tilting bundle. We show that this tilting bundle has a quasi-hereditary endomorphism ring and we identify the standard, costandard, projective and simple modules of the latter.
be a base commutative ring,
a commutative ring of coefficients,
a quasi-compact quasi-separated
a sheaf of Azumaya algebras over
. Under the assumption that
, we prove that the noncommutative motives with
are isomorphic. As an application, we conclude that a similar
isomorphism holds for every
-linear additive invariant. This leads to several computations.
Along the way we show that, in the case of finite-dimensional algebras of finite
global dimension, all additive invariants are nilinvariant.
In a recent paper, Iyama and Yoshino considered two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen–Macaulay modules in terms of linear algebra data. In this paper, we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov’s result on the graded singularity category.
In this paper we discuss some of the recent developments on derived equivalences in algebraic geometry.
In this paper we discuss some of the recent developments on derived equivalences in algebraic geometry but we don't intend to give any kind of comprehensive survey. It is better to regard this paper as a set of pointers to some of the recent literature.
To put the subject in context we start with some historical background. Derived (and triangulated) categories were introduced by Verdier in his thesis (see [26, 79]) in order to simplify homological algebra. From this point of view the role of derived categories is purely technical.
The first non-trivial derived equivalence in the literature is between the derived categories of sheaves on a sphere bundle and its dual bundle . The equivalence resembles Fourier-transform and is now known as a “Fourier-Sato” transform.
The first purely algebro-geometric derived equivalence seems to appear in  where is it is shown that an abelian variety A and its dual Â have equivalent derived categories of coherent sheaves. Again the equivalence is similar to a Fourier-transform and is therefore called a “Fourier-Mukai” transform.
In  Beilinson showed that ℙn is derived equivalent to a (noncommutative) finite dimensional algebra. This explained earlier results by Barth and Hulek on the relation between vector bundles and linear algebra. Beilinson's result has been generalized to other varieties and has evolved into the theory of exceptional sequences (see for example ).
Email your librarian or administrator to recommend adding this to your organisation's collection.