Riemann-Roch for equivariant Chow groups
Dan Edidin,William Graham +1 more
Abstract:
The purpose of this paper is to prove an equivariant Riemann-Roch theorem for schemes or algebraic spaces with an action of a linear algebraic group $G$. For a $G$-space $X$, this theorem gives an isomorphism between a completion of the equivariant Grothendieck group and a completion of equivariant equivariant Chow groups.
The key to proving this isomorphism is a geometric description of completions of the equivariant Grothendieck group. Besides Riemann-Roch, this result has some purely $K$-theoretic applications. In particular, we prove a conjecture of K\"ock (in the case of regular schemes) and extend to arbitrary characteristic a result of Segal on representation rings.read more
Citations
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Uniform k-stability, duistermaat-heckman measures and singularities of pairs
TL;DR: In this paper, a formalism inspired from non-archimedean geometry to study K-stability was proposed, where the Donaldson-Futaki invariant is interpreted as the non-Archimediean version of the Mabuchi functional, up to an explicit error term.
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Uniform K-stability, Duistermaat-Heckman measures and singularities of pairs
TL;DR: In this paper, a formalism inspired from non-archimedean geometry to study K-stability was proposed, where the Donaldson-Futaki invariant is interpreted as the non-Archimediean version of the Mabuchi functional, up to an explicit error term.
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Moduli of twisted sheaves
TL;DR: In this paper, the authors studied moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces and showed that they are asympotically geometrically irreducible, normal, generically smooth, and l.c.i.
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Degenerate Cohomological Hall algebra and quantized Donaldson-Thomas invariants for m-loop quivers
TL;DR: In this article, a combinatorial formula for quantized Donaldson-Thomas invariants of the m-loop quiver was derived, using the combinatorics of noncommutative Hilbert schemes and a degenerate version of the Cohomological Hall algebra of this quiver.
Proceedings ArticleDOI
A Survey of Characteristic Classes of Singular Spaces
Jörg Schürmann,Shoji Yokura +1 more
References
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Linear algebraic groups
TL;DR: Conventions and notation background material from algebraic geometry general notions associated with algebraic groups homogeneous spaces solvable groups Borel subgroups reductive groups rationality questions are discussed in this paper.
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Éléments de géométrie algébrique : IV. Étude locale des schémas et des morphismes de schémas, Troisième partie
Journal Article
Éléments de géométrie algébrique : II. Étude globale élémentaire de quelques classes de morphismes
TL;DR: In this article, the authors present a legal opinion on the use of commercial or impression systématiques in the context of the publication of books of the I.H.É.S.