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Paper Citation Record · LEDGER

On the injective dimension of unit Cartier and Frobenius modules

As of 12 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2412.08423.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.08423 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:04:46.275325Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

28 of 28 outbound references displayed

  • verified exact2
  • verified fuzzy25
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8bc7605e-b725-4146-9b6a-5f59a40600cc · outbound

This paper cites Alvarez-Montaner, M.

On the injective dimension of unit Cartier and Frobenius modules Alvarez-Montaner, M

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.671119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.163557Z digest=sha256:6be49addade0c78d1b94379e6b174420beabbcbd867b1096934f0e8375559c4f

Observation 48e5727e-c2e7-466c-8fc9-ad4b6de206e5 · outbound

This paper cites Bhatt, M.

On the injective dimension of unit Cartier and Frobenius modules Bhatt, M

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.658900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.170083Z digest=sha256:8fb6e3a09880213d6c2ddeea4a4d3147bc6a95320dcc41d867c033b5a53d829b

Observation 5b5f75a6-04e0-4a17-bcd6-8d5fa9091129 · outbound

This paper cites Bhatt, J.

On the injective dimension of unit Cartier and Frobenius modules Bhatt, J

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.647200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.174266Z digest=sha256:f060c8d5277baa235fdc40ec4abfa963a359885812002c8a2071935a1ef9d1a6

Observation 60ae1335-1ede-4d77-b962-fa1bccfda10f · outbound

This paper cites Blickle : The D -module structure of R[F] -modules , Trans.

On the injective dimension of unit Cartier and Frobenius modules Blickle : The D -module structure of R[F] -modules , Trans

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.636623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.179035Z digest=sha256:0a27b7f2f20057fb93550a6e214a16dc07662da5b52047a14a219a1b98ca558b

Observation d1fb70a7-ac01-43a1-add9-bcd61f864d26 · outbound

This paper cites Blickle : Minimal --sheaves, Algebra and Number Theory 2 (2008), no.

On the injective dimension of unit Cartier and Frobenius modules Blickle : Minimal --sheaves, Algebra and Number Theory 2 (2008), no

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.625630Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.183445Z digest=sha256:ad34d03cad5453d2469d7291b0eb8ac7b776a72cf03b21724bebefbb6c1b2d13

Observation 265a15e6-cb4e-4342-b720-27c564ae4d9a · outbound

This paper cites Blickle and G.

On the injective dimension of unit Cartier and Frobenius modules Blickle and G

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.614562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.187659Z digest=sha256:863e69e4c09004a5e95ad91ac92b7ca03da31a0b38b063141bf48004e5de1d17

Observation d4b956b2-7d4e-4fa4-a1aa-18bcef2f05a9 · outbound

This paper cites Cartier Crystals.

On the injective dimension of unit Cartier and Frobenius modules Cartier Crystals

Reference 7

Resolution
verified exact
local_arxiv, observed 2026-08-11T18:04:46.337386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.192099Z digest=sha256:34264a5c8364b0c0c30b0ead4304a2df7afb290628bbab9bcbe55db9d0b30661

Observation 5e0724ae-dc13-476e-9013-7c52b2f2131c · outbound

This paper cites Cartier Crystals have finite global dimension.

On the injective dimension of unit Cartier and Frobenius modules Cartier Crystals have finite global dimension

Reference 8

Resolution
verified exact
local_arxiv, observed 2026-08-11T18:04:46.318911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.196566Z digest=sha256:4ba0d2dec52bddd3a369adbdcdee83b4452c1c5a448e584ce2c10899c78f9902

Observation fe85e89d-1e87-40ac-8008-87db39ed03b2 · outbound

This paper cites Bhatt, M.

On the injective dimension of unit Cartier and Frobenius modules Bhatt, M

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.602726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.201460Z digest=sha256:b6c2cbe45b3870512351f54aa3d9649bcef81fc9933927abc6c1c205ced45ed8

Observation 3a788a59-fe62-49a0-8521-723bf92405ed · outbound

This paper cites Emerton and M.

On the injective dimension of unit Cartier and Frobenius modules Emerton and M

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.590859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.205384Z digest=sha256:14986d6f4d8e23a69d7f888c84e6390468624fa3dc0f44c64f8d738c5d5f6255

Observation 1b6a681e-a7ae-40cb-bae3-b5f212b5daf3 · outbound

This paper cites Gabber : Notes on some t -structures , Geometric aspects of D work theory.

On the injective dimension of unit Cartier and Frobenius modules Gabber : Notes on some t -structures , Geometric aspects of D work theory

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.578796Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.209113Z digest=sha256:7e05078208bed2155a910bab1303e2fd98eac412293852e3b89cdb2d8f67b1b0

Observation 68f2e301-3f49-4d75-83fc-aea0fff36222 · outbound

This paper cites Hartshorne and R.

On the injective dimension of unit Cartier and Frobenius modules Hartshorne and R

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.566131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.213025Z digest=sha256:311261cad7aa1a31d3feed5141fce992bb2807c78c32f503b0fa399730a3a8e4

Observation c01913fa-f98e-458d-8509-d28c20f00b20 · outbound

This paper cites Hochster : Some finiteness properties of L yubeznik's F -modules , Algebra, geometry and their interactions, Contemp.

On the injective dimension of unit Cartier and Frobenius modules Hochster : Some finiteness properties of L yubeznik's F -modules , Algebra, geometry and their interactions, Contemp

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.554766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.217049Z digest=sha256:9bb6620ce2da92aff2236aa0e96df783abe8fafdffb1378ab88d6ff1e96b69d1

Observation 254431a1-2afc-4191-aced-c3cbc9c9a850 · outbound

This paper cites an unresolved cited work.

On the injective dimension of unit Cartier and Frobenius modules Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-11T18:04:46.543505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.220922Z digest=sha256:818f4ac1b890a75953b4f86b2d857c9c6251d82fd140b31188f838dab61098fb

Observation b4ca616c-a84d-452a-a135-3716698984b6 · outbound

This paper cites Katzman, L.

On the injective dimension of unit Cartier and Frobenius modules Katzman, L

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.528602Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.224789Z digest=sha256:3363cdfc4ac48e68e085c59bd5437e1a2d662ad1fc3c2a785bccc937db61a854

Observation 961ca978-b9a2-4e07-829c-07e0bcd4dd18 · outbound

This paper cites Katzman and W.

On the injective dimension of unit Cartier and Frobenius modules Katzman and W

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.516537Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.228366Z digest=sha256:fde6cad7b84894f0b8261906b01b491cb489136e056f4ec827ecb9aae7e2d205

Observation 0e8b2c41-7ffb-42c0-bdb0-428bf558454d · outbound

This paper cites Kunz : Characterizations of regular local rings for characteristic p , Amer.

On the injective dimension of unit Cartier and Frobenius modules Kunz : Characterizations of regular local rings for characteristic p , Amer

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.505815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.232190Z digest=sha256:aa50e799bd8a22005219b451fa93113873dd75122eff9693b5f6240da70aef1f

Observation 81fb21c2-675e-4f9f-a4a8-4a7e19cd6a12 · outbound

This paper cites Lyubeznik : F -modules: applications to local cohomology and D -modules in characteristic p>0 , J.

On the injective dimension of unit Cartier and Frobenius modules Lyubeznik : F -modules: applications to local cohomology and D -modules in characteristic p>0 , J

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.494463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.235672Z digest=sha256:34910742e1bc7b52052ecf6a870d9d6351bb978ab9301f0491ff7733b449619f

Observation 93992295-6c50-4421-bd4f-ba6585cdd978 · outbound

This paper cites Lyubeznik : On some local cohomology invariants of local rings, Math.

On the injective dimension of unit Cartier and Frobenius modules Lyubeznik : On some local cohomology invariants of local rings, Math

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.482313Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.239339Z digest=sha256:c14625f8c59743b93d2d4d1955b3f6d9f0449a7c8d2fd966b9c83214724458ff

Observation 5ed04478-4115-431a-a884-5daa2687cb45 · outbound

This paper cites Lyubeznik : On the vanishing of local cohomology in characteristic p>0 , Compos.

On the injective dimension of unit Cartier and Frobenius modules Lyubeznik : On the vanishing of local cohomology in characteristic p>0 , Compos

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.467830Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.242880Z digest=sha256:d9b0773b02fcb51e78d84fa79c1ba55411541bfc08f48f2ebbe94f22c66d4630

Observation c3eeee80-4db9-42cb-9969-d2a6f15d24b6 · outbound

This paper cites Lyubeznik, A.

On the injective dimension of unit Cartier and Frobenius modules Lyubeznik, A

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.453556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.248634Z digest=sha256:3f892e0931a54fedabf7eadacecc918b889fb236b3cbc21ec08f1d9c8364bf74

Observation 58125f0a-d7ca-4616-87d4-3dfa0e1094c4 · outbound

This paper cites Ma : The category of F -modules has finite global dimension , J.

On the injective dimension of unit Cartier and Frobenius modules Ma : The category of F -modules has finite global dimension , J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.440150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.252559Z digest=sha256:5c4cce68a71d7a400dfa3861805128545f0b844ffd479aaf5a00eed771e28ae4

Observation fb293649-a048-4288-913e-f7c1c738c9b8 · outbound

This paper cites Ma and W.

On the injective dimension of unit Cartier and Frobenius modules Ma and W

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.425143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.256406Z digest=sha256:90d4dca0f98a7b1ccaac7033eed194d2dea43a7d743e43a6725a9bede2735505

Observation 9779b0a3-d1ce-4275-88f8-cabc4178e573 · outbound

This paper cites Peskine and L.

On the injective dimension of unit Cartier and Frobenius modules Peskine and L

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.409460Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.260265Z digest=sha256:c24a77fe9428fdd680e50cd95a0e770943b13cb4bee9f5fd494c11f7638e75a1

Observation 386a25b9-690c-41ff-b9db-f5a75a8a0f41 · outbound

This paper cites Switala and W.

On the injective dimension of unit Cartier and Frobenius modules Switala and W

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.389645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.264256Z digest=sha256:ea0e5e9c8052d41845a0d0af8001a4d95849b7c44cb5383f2666319f2cea6dcf

Observation afcad804-8973-4c25-8d5e-16c1a9d170ef · outbound

This paper cites Zhang : Lyubeznik numbers of projective schemes, Adv.

On the injective dimension of unit Cartier and Frobenius modules Zhang : Lyubeznik numbers of projective schemes, Adv

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.377614Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.268022Z digest=sha256:8171f6015d5fd77fa95454df0ead8a1ca566b65d6337a82babbcf144ed5a8d48

Observation 6e3a2eeb-858c-4389-bb91-2c163196aa50 · outbound

This paper cites Zhang : On injective dimension of F -finite F -modules and holonomic D -modules , Bull.

On the injective dimension of unit Cartier and Frobenius modules Zhang : On injective dimension of F -finite F -modules and holonomic D -modules , Bull

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.364546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.271652Z digest=sha256:e317f60de0bc4bfe40ff1536222c90bafa84d6d808866dfdbfaae98cdf600969

Observation 728f3fa6-d348-4a9d-a0ab-f24e4a93b454 · outbound

This paper cites Zhang : F^e -modules with applications to D -modules , J.

On the injective dimension of unit Cartier and Frobenius modules Zhang : F^e -modules with applications to D -modules , J

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T18:04:46.350621Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-11T18:04:46.275325Z digest=sha256:83f031ff41c65e9f7fdd6fc1dd43aee867470b9592a419d595910a1c9d2d5339

Pith citing papers

No inbound Pith citation observations are available.