Mod-m and profinite higher K-theory of exact categories, orders, and groupings

Keyword(s):  
K Theory ◽  
2019 ◽  
Vol 296 (1-2) ◽  
pp. 147-167
Author(s):  
Chris Eppolito ◽  
Jaiung Jun ◽  
Matt Szczesny

Topology ◽  
2004 ◽  
Vol 43 (5) ◽  
pp. 1089-1103 ◽  
Author(s):  
Marco Schlichting
Keyword(s):  
K Theory ◽  

Author(s):  
Marco Schlichting

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.


Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  

1973 ◽  
Vol 6 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Pramod K. Sharma ◽  
Jan R. Strooker
Keyword(s):  

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.


Author(s):  
Andrei Neguţ

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.


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