Geodesic
Factorization Statistics and the Twisted Grothendieck-Lefschetz formula
Séminaire lotharingien de combinatoire, 80B (2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

Factorization statistics are functions defined on the set Polyd(Fq) of all monic degree d polynomials with coefficients in Fq which only depend on the degrees of the irreducible factors of a polynomial. We show that the expected values of factorization statistics are determined by the representation theoretic structure of the cohomology of point configurations in R3. This twisted Grothendieck-Lefschetz formula for Polyd is analogous to a result of Church, Ellenberg, and Farb for squarefree polynomials. Our proof uses formal power series methods which also lead to a new proof of the Church, Ellenberg, and Farb result circumventing algebraic geometry. 

@article{SLC_2018_80B_a5,
     author = {Trevor Hyde},
     title = {Factorization {Statistics} and the {Twisted} {Grothendieck-Lefschetz} formula},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {80B},
     year = {2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/}
}
TY  - JOUR
AU  - Trevor Hyde
TI  - Factorization Statistics and the Twisted Grothendieck-Lefschetz formula
JO  - Séminaire lotharingien de combinatoire
PY  - 2018
VL  - 80B
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/
ID  - SLC_2018_80B_a5
ER  - 
%0 Journal Article
%A Trevor Hyde
%T Factorization Statistics and the Twisted Grothendieck-Lefschetz formula
%J Séminaire lotharingien de combinatoire
%D 2018
%V 80B
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/
%F SLC_2018_80B_a5
Trevor Hyde. Factorization Statistics and the Twisted Grothendieck-Lefschetz formula. Séminaire lotharingien de combinatoire, 80B (2018). http://geodesic.mathdoc.fr/item/SLC_2018_80B_a5/