Cartier modules: finiteness results
On a locally Noetherian scheme X over a field of positive characteristic p , we study the category of coherent X -modules M equipped with a p e -linear map, i.e. an additive map C : X X satisfying rC ( m ) C ( r p e m ) for all m M , r X . The notion of nilpotence, meaning that some power of the map...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
1. Dezember 2011
|
| In: |
Journal für die reine und angewandte Mathematik
Year: 2011, Heft: 661, Pages: 85-123 |
| ISSN: | 1435-5345 |
| DOI: | 10.1515/CRELLE.2011.087 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1515/CRELLE.2011.087 Verlag, lizenzpflichtig, Volltext: https://www.degruyterbrill.com/document/doi/10.1515/CRELLE.2011.087/html 
|
| Verfasserangaben: | by Manuel Blickle at Mainz and Gebhard Böckle at Heidelberg |
MARC
| LEADER | 00000caa a2200000 c 4500 | ||
|---|---|---|---|
| 001 | 179704480X | ||
| 003 | DE-627 | ||
| 005 | 20250530002959.0 | ||
| 007 | cr uuu---uuuuu | ||
| 008 | 220330s2011 xx |||||o 00| ||eng c | ||
| 024 | 7 | |a 10.1515/CRELLE.2011.087 |2 doi | |
| 035 | |a (DE-627)179704480X | ||
| 035 | |a (DE-599)KXP179704480X | ||
| 035 | |a (OCoLC)1341458257 | ||
| 040 | |a DE-627 |b ger |c DE-627 |e rda | ||
| 041 | |a eng | ||
| 084 | |a 27 |2 sdnb | ||
| 100 | 1 | |a Blickle, Manuel |e VerfasserIn |0 (DE-588)1247778541 |0 (DE-627)1782389679 |4 aut | |
| 245 | 1 | 0 | |a Cartier modules |b finiteness results |c by Manuel Blickle at Mainz and Gebhard Böckle at Heidelberg |
| 264 | 1 | |c 1. Dezember 2011 | |
| 300 | |a 39 | ||
| 336 | |a Text |b txt |2 rdacontent | ||
| 337 | |a Computermedien |b c |2 rdamedia | ||
| 338 | |a Online-Ressource |b cr |2 rdacarrier | ||
| 500 | |a Gesehen am 30.03.2022 | ||
| 520 | |a On a locally Noetherian scheme X over a field of positive characteristic p , we study the category of coherent X -modules M equipped with a p e -linear map, i.e. an additive map C : X X satisfying rC ( m ) C ( r p e m ) for all m M , r X . The notion of nilpotence, meaning that some power of the map C is zero, is used to rigidify this category. The resulting quotient category, called Cartier crystals, satisfies some strong finiteness conditions. The main result in this paper states that, if the Frobenius morphism on X is a finite map, i.e. if X is F -finite, then all Cartier crystals have finite length. We further show how this and related results can be used to recover and generalize other finiteness results of HartshorneSpeiser Ann. Math. 105: 4579, 1977, Lyubeznik J. reine angew. Math. 491: 65130, 1997, Sharp Trans. Amer. Math. Soc. 359: 42374258, 2007, EnescuHochster Alg. Num. Th. 2: 721754, 2008, and Hochster Contemp. Math. 448: 119127, 2007 about the structure of modules with a left action of the Frobenius. For example, we show that over any regular F -finite scheme X Lyubeznik's F -finite modules J. reine angew. Math. 491: 65130, 1997 have finite length. | ||
| 700 | 1 | |a Böckle, Gebhard |d 1964- |e VerfasserIn |0 (DE-588)1052651798 |0 (DE-627)788915908 |0 (DE-576)408431660 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Journal für die reine und angewandte Mathematik |d Berlin : de Gruyter, 1826 |g (2011), 661, Seite 85-123 |h Online-Ressource |w (DE-627)266887171 |w (DE-600)1468592-9 |w (DE-576)07987598X |x 1435-5345 |7 nnas |a Cartier modules finiteness results |
| 773 | 1 | 8 | |g year:2011 |g number:661 |g pages:85-123 |g extent:39 |a Cartier modules finiteness results |
| 856 | 4 | 0 | |u https://doi.org/10.1515/CRELLE.2011.087 |x Verlag |x Resolving-System |z lizenzpflichtig |3 Volltext |
| 856 | 4 | 0 | |u https://www.degruyterbrill.com/document/doi/10.1515/CRELLE.2011.087/html |x Verlag |z lizenzpflichtig |3 Volltext |
| 951 | |a AR | ||
| 992 | |a 20220330 | ||
| 993 | |a Article | ||
| 994 | |a 2011 | ||
| 998 | |g 1052651798 |a Böckle, Gebhard |m 1052651798:Böckle, Gebhard |d 110000 |d 110100 |d 110000 |d 110400 |e 110000PB1052651798 |e 110100PB1052651798 |e 110000PB1052651798 |e 110400PB1052651798 |k 0/110000/ |k 1/110000/110100/ |k 0/110000/ |k 1/110000/110400/ |p 2 |y j | ||
| 999 | |a KXP-PPN179704480X |e 4106966662 | ||
| BIB | |a Y | ||
| SER | |a journal | ||
| JSO | |a {"person":[{"role":"aut","display":"Blickle, Manuel","roleDisplay":"VerfasserIn","given":"Manuel","family":"Blickle"},{"roleDisplay":"VerfasserIn","role":"aut","display":"Böckle, Gebhard","family":"Böckle","given":"Gebhard"}],"name":{"displayForm":["by Manuel Blickle at Mainz and Gebhard Böckle at Heidelberg"]},"physDesc":[{"extent":"39 S."}],"note":["Gesehen am 30.03.2022"],"id":{"eki":["179704480X"],"doi":["10.1515/CRELLE.2011.087"]},"recId":"179704480X","type":{"media":"Online-Ressource","bibl":"article-journal"},"language":["eng"],"title":[{"title":"Cartier modules","title_sort":"Cartier modules","subtitle":"finiteness results"}],"origin":[{"dateIssuedDisp":"1. Dezember 2011","dateIssuedKey":"2011"}],"relHost":[{"pubHistory":["1.1826 -"],"note":["Gesehen am 06.09.2018"],"physDesc":[{"extent":"Online-Ressource"}],"recId":"266887171","id":{"doi":["10.1515/crll"],"eki":["266887171"],"zdb":["1468592-9"],"issn":["1435-5345"]},"type":{"bibl":"periodical","media":"Online-Ressource"},"origin":[{"publisher":"de Gruyter","publisherPlace":"Berlin","dateIssuedKey":"1826","dateIssuedDisp":"1826-"}],"title":[{"subtitle":"the world's oldest mathematical periodical","title_sort":"Journal für die reine und angewandte Mathematik","title":"Journal für die reine und angewandte Mathematik"}],"titleAlt":[{"title":"Crelle's journal"},{"title":"Crelles journal"}],"language":["ger","eng","fre"],"part":{"issue":"661","year":"2011","extent":"39","pages":"85-123","text":"(2011), 661, Seite 85-123"},"disp":"Cartier modules finiteness resultsJournal für die reine und angewandte Mathematik"}]} | ||
| SRT | |a BLICKLEMANCARTIERMOD1201 | ||