Perverse sheaves on Riemann surfaces as Milnor sheaves
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423000841/type/journal_article |
| _version_ | 1797665247039848448 |
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| author | Tobias Dyckerhoff Mikhail Kapranov Yan Soibelman |
| author_facet | Tobias Dyckerhoff Mikhail Kapranov Yan Soibelman |
| author_sort | Tobias Dyckerhoff |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T19:41:12Z |
| format | Article |
| id | doaj.art-1759d0843f564faaa922b0707316e669 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-11T19:41:12Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-1759d0843f564faaa922b0707316e6692023-10-06T09:27:56ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.84Perverse sheaves on Riemann surfaces as Milnor sheavesTobias Dyckerhoff0Mikhail Kapranov1Yan Soibelman2Universität Hamburg, Fachbereich Mathematik, Bundesstrasse 55, 20146 Hamburg, Germany; E-mail:Kavli IPMU (WPI), UTIAS, The University of Tokyo, Kashiwa, Chiba, 277-8583 Japan; E-mail:Dept. Math., Kansas State University, Manhattan, KS 66506 USA; E-mail: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.https://www.cambridge.org/core/product/identifier/S2050509423000841/type/journal_article32S6014F0818N2518N60 |
| spellingShingle | Tobias Dyckerhoff Mikhail Kapranov Yan Soibelman Perverse sheaves on Riemann surfaces as Milnor sheaves Forum of Mathematics, Sigma 32S60 14F08 18N25 18N60 |
| title | Perverse sheaves on Riemann surfaces as Milnor sheaves |
| title_full | Perverse sheaves on Riemann surfaces as Milnor sheaves |
| title_fullStr | Perverse sheaves on Riemann surfaces as Milnor sheaves |
| title_full_unstemmed | Perverse sheaves on Riemann surfaces as Milnor sheaves |
| title_short | Perverse sheaves on Riemann surfaces as Milnor sheaves |
| title_sort | perverse sheaves on riemann surfaces as milnor sheaves |
| topic | 32S60 14F08 18N25 18N60 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423000841/type/journal_article |
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