Perverse sheaves on Riemann surfaces as Milnor sheaves
Forum of Mathematics, Sigma, Tome 11 (2023)
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Constructible sheaves of abelian groups on a stratified space can be equivalently described in terms of representations of the exit-path category. In this work, we provide a similar presentation of the abelian category of perverse sheaves on a stratified surface in terms of representations of the so-called paracyclic category of the surface. The category models a hybrid exit–entrance behaviour with respect to chosen sectors of direction, placing it ‘in between’ exit and entrance path categories. In particular, this perspective yields an intrinsic definition of perverse sheaves as an abelian category without reference to derived categories and t-structures.
@article{10_1017_fms_2023_84,
author = {Tobias Dyckerhoff and Mikhail Kapranov and Yan Soibelman},
title = {Perverse sheaves on {Riemann} surfaces as {Milnor} sheaves},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {11},
year = {2023},
doi = {10.1017/fms.2023.84},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.84/}
}
TY - JOUR AU - Tobias Dyckerhoff AU - Mikhail Kapranov AU - Yan Soibelman TI - Perverse sheaves on Riemann surfaces as Milnor sheaves JO - Forum of Mathematics, Sigma PY - 2023 VL - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.84/ DO - 10.1017/fms.2023.84 LA - en ID - 10_1017_fms_2023_84 ER -
%0 Journal Article %A Tobias Dyckerhoff %A Mikhail Kapranov %A Yan Soibelman %T Perverse sheaves on Riemann surfaces as Milnor sheaves %J Forum of Mathematics, Sigma %D 2023 %V 11 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.84/ %R 10.1017/fms.2023.84 %G en %F 10_1017_fms_2023_84
Tobias Dyckerhoff; Mikhail Kapranov; Yan Soibelman. Perverse sheaves on Riemann surfaces as Milnor sheaves. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.84
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