Pith. Sign in

RECORD

Contramodules for algebraic groups: induction and projective covers

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Dylan Johnston

Representation Theory · Submitted 15 Apr 2023

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Firstly, we show that induction of contramodules over coordinate rings of algebraic groups is exact if and only if the associated quotient variety is affine.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2304.07525 (version 3)
Pith IDF2DVXB6B, Pith's permanent record of this paper and its review
CitationDylan Johnston. "Contramodules for algebraic groups: induction and projective covers." arXiv:2304.07525 (2023). https://pith.science/paper/F2DVXB6B
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,602 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.82 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

In this paper we will investigate contramodules for algebraic groups. Namely, we give contra-analogs to two 20th century results about comodules. Firstly, we show that induction of contramodules over coordinate rings of algebraic groups is exact if and only if the associated quotient variety is affine. Secondly, we give an inverse limit theorem for constructing projective covers of simple $G$-modules using $G$-structures of projective covers of simple modules for the first Frobenius kernel, $G_1$.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this paper we will investigate contramodules for algebraic groups. contribution 0.68 0.56 0.03 asserted 0.57
s1 Namely, we give contra-analogs to two 20th century results about comodules. contribution 0.97 0.87 0.11 asserted 0.97
s2 Firstly, we show that induction of contramodules over coordinate rings of algebraic groups is exact if and only if the associated quotient variety is affine. result 0.99 0.95 0.30 asserted 1.00
s3 Secondly, we give an inverse limit theorem for constructing projective covers of simple $G$-modules using $G$-structures of projective covers of simple modules for the first Frobenius kernel, $G_1$. result 0.69 0.95 0.20 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In this paper we will investigate contramodules for algebraic groups. Namely, we give contra-analogs to two 20th century results about comodules. Firstly, we show that induction of contramodules over coordinate rings of algebraic groups is exact if and only if the associated quotient variety is affine. Secondly, we give an inverse limit theorem for constructing projective covers of simple $G$-modules using $G$-structures of projective covers of simple modules for the first Frobenius kernel, $G_1$.

Human review

How Pith checks papers → · Full audit of this paper →

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.