The convolution ring $K^{GL_n(\mathcal{O})\rtimes\mathbb{C}^\times}(\mathrm{Gr}_{GL_n})$ was identified with a quantum unipotent cell of the loop group $LSL_2$ in [Cautis-Williams, J. Amer. Math. Soc. 32 (2019), pp. 709-778]. We identify basis formed by classes irreducible equivariant perverse coherent sheaves dual canonical cell.

Cell cycle ends with cytokinesis that is the physical separation of a cell into two daughter cells. For faithful cytokinesis, cells integrate multiple processes, such as actomyosin ring formation, contraction and plasma membrane closure, into coherent responses. Linear actin assembly by formins is essential for formation and maintenance of actomyosin ring. Although budding yeast's two formins, ...

We present ideas for a storage ring dedicated to and optimized for the production of synchrotron radiation over the infrared wavelength range from 1-1000 μm. The site for the 66 m circumference ring is atop the existing ALS booster synchrotron shielding. This area provides enough floor space for both the ring and beamlines, and hutches. We plan to operate the ring in two modes: as a conventiona...

The two beams of the 2 GeV Stanford electron-positron storage ring can exhibit, under certain modes of operation, coherent oscillations which have a rate of growth proportional to the beam current. Since this rate is much slower than the machine revolution tiequency, it is possible to produce damping by means of negative feedback, the beam itself being part of the feedback loop. Three systems h...

1.1. Background. The goal of this paper is to investigate algebraic stacks through their associated categories of quasi-coherent sheaves (or, better, complexes). To put this investigation in context, note that an affine scheme is completely determined by its ring of functions. Using merely the ring of functions, though, it is difficult to move beyond affine schemes. However, if one is willing t...

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.

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 isomorphism classes of indecomposable injective modules are used in an essential way.

Let D denote the open unit disk in C centered at 0 . Let H∞ R denote the set of all bounded and holomorphic functions defined in D that also satisfy f (z) = f (z) for all z ∈ D . It is shown that H∞ R is a coherent ring. Mathematics subject classification (2010): Primary 30A98; Secondary 46J15, 93B25, 16S15.

We introduce the concept of the ghost dimension gh. dim. R of a ring R. This is the longest nontrivial chain of maps in the derived category emanating from a perfect complex such that each map is zero on homology. We show that gh. dim. R ≤ w. dim. R, with equality if R is coherent or w. dim. R = 1.

We construct an invariant of t-structures on the derived category of a Noetherian ring. This invariant is complete when restricting to the category of quasi-coherent complexes, and also gives a classification of nullity classes with the same restriction. On the full derived category of Z we show that the class of distinct t-structures do not form a set.