scholarly journals On the K-Theory of the Coordinate Axes in the Plane

2007 ◽  
Vol 185 ◽  
pp. 93-109 ◽  
Author(s):  
Lars Hesselholt
Keyword(s):  
Intersection Point ◽  
Coordinate Ring ◽  
De Rham ◽  
K Theory ◽  
Witt Groups ◽  
The Ideal

AbstractLet k a regular noetherian p-algebra, let A = k[x, y]/(xy) be the coordinate ring of the coordinate axes in the affine k-plane, and let I = (x,y) be the ideal that defines the intersection point. We evaluate the relative K-groups Kq(A, I) completely in terms of the big de Rham-Witt groups of k. This generalizes a formula for K1(A, I) and K2(A, I) by Dennis and Krusemeyer.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals Twisted K-theory, Real A-bundles and Grothendieck–Witt groups

2017 ◽  
Vol 221 (7) ◽  
pp. 1629-1640 ◽  
Author(s):  
Max Karoubi ◽  
Charles Weibel
Keyword(s):  
K Theory ◽  
Witt Groups

scholarly journals Semi-infinite Plücker Relations and Weyl Modules

2018 ◽  
Vol 2020 (14) ◽  
pp. 4357-4394 ◽  
Author(s):  
Evgeny Feigin ◽  
Ievgen Makedonskyi
Keyword(s):  
Type A ◽  
Character Formula ◽  
Flag Varieties ◽  
Coordinate Ring ◽  
Weyl Modules ◽  
Plücker Relations ◽  
Plücker Embedding ◽  
Formal Version ◽  
The Ideal

Abstract The goal of this paper is two-fold. First, we write down the semi-infinite Plücker relations, describing the Drinfeld–Plücker embedding of the (formal version of) semi-infinite flag varieties in type A. Second, we study the homogeneous coordinate ring, that is, the quotient by the ideal generated by the semi-infinite Plücker relations. We establish the isomorphism with the algebra of dual global Weyl modules and derive a new character formula.

CLASSIFICATION OF EXTENSIONS OF A𝕋-ALGEBRAS

2011 ◽  
Vol 22 (08) ◽  
pp. 1187-1208 ◽  
Author(s):  
CHANGGUO WEI
Keyword(s):  
Exact Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
K Theory ◽  
Necessary And Sufficient ◽  
The Ideal

We classify certain extensions of A𝕋-algebras using the six-term exact sequence in K-theory together with the Elliott invariants of the ideal and quotient. We also give certain necessary and sufficient conditions for such extension algebras being A𝕋-algebras.

On the K-theory of elliptic curves

1999 ◽  
Vol 1999 (507) ◽  
pp. 81-91
Author(s):  
Kevin P Knudson
Keyword(s):  
Elliptic Curve ◽  
Elliptic Curves ◽  
Number Field ◽  
Function Field ◽  
Coordinate Ring ◽  
Infinite Field ◽  
Closed Point ◽  
K Theory

Abstract Let A be the coordinate ring of an affine elliptic curve (over an infinite field k) of the form X – {p}, where X is projective and p is a closed point on X. Denote by F the function field of X. We show that the image of H.(GL2 (A), ℤ) in H.(GL2 (F), ℤ) coincides with the image of H.(GL2 (k), ℤ). As a consequence, we obtain numerous results about the K-theory of A and X. For example, if k is a number field, we show that r2 (K2 (A) ⊗ ℚ) = 0, where rm denotes the mth level of the rank filtration.

Hermitian K-theory of exact categories

2009 ◽  
Vol 5 (1) ◽  
pp. 105-165 ◽  
Author(s):  
Marco Schlichting
Keyword(s):  
Bilinear Forms ◽  
K Theory ◽  
Witt Groups ◽  
Exact Categories

AbstractWe study the theory of higher Grothendieck-Witt groups, alias algebraic hermitian K-theory, of symmetric bilinear forms in exact categories, and prove additivity, cofinality, dévissage and localization theorems – preparing the ground for the theory of higher Grothendieck-Witt groups of schemes as developed in [Sch08a] and [Sch08b]. No assumption on the characteristic is being made.

scholarly journals AT structure of AH algebras with the ideal property and torsion free K-theory

2010 ◽  
Vol 258 (6) ◽  
pp. 2119-2143 ◽  
Author(s):  
Guihua Gong ◽  
Chunlan Jiang ◽  
Liangqing Li ◽  
Cornel Pasnicu
Keyword(s):  
K Theory ◽  
Ideal Property ◽  
Torsion Free ◽  
The Ideal
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