Counting rational points of quiver moduli

By Markus Reineke. 2005

64 citations recorded by the source corpus.

It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2afc57b2b6eba6f33b49b3eb73ce0b605eb5eb7b

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In Algebra and Number Theory

1. Philippe Caldero
2. Frédéric Chapoton
3. I. Reiten
4. B. Keller
5. Markus Reineke
6. Ralf Schiffler
7. J. Engel
8. Aslak Bakke Buan

In Geometry and Topology

1. Markus Reineke
2. Philippe Caldero
3. B. Keller
4. Frédéric Chapoton
5. I. Reiten
6. J. Engel
7. Ralf Schiffler
8. Aslak Bakke Buan

In Statistical and Nonlinear Physics

1. Frédéric Chapoton
2. Philippe Caldero
3. J. Engel
4. Markus Reineke
5. B. Keller
6. Ralf Schiffler
7. Bernard Leclerc
8. I. Reiten

Citations in the corpus

• Cluster algebras as Hall algebras of quiver representations (2004, methodology): “In order to calculate the Euler–Poincaré characteristic of Grassmannians, we will use the following classical lemma, see [Rei], which is an application of Grothendieck–Lefschetz’s fixed point formula for the Frobenius in étale cohomology.”
• Smooth models of quiver moduli (2007, methodology): “This defines an associative unital NI-graded Q-algebra by [15].”
• On the quiver Grassmannian in the acyclic case (2006, background): “The integral is in fact a C-algebra homomorphism by [20].”
• Moduli of representations of quivers (2008, methodology): “Then we can define the evaluation morphism as in [56]:”