Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations

Rui Chen

RECORD

Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations

Rui Chen

Representation Theory · Submitted 22 Mar 2023

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

The authors' main claim In this paper we prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

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, 2,949 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.20 · compares with prior results 0.14 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad. In particular, this implies a conjectural Euler--Poincar\'e characteristic formula for Gan--Gross--Prasad models. Besides, we also single out a special class of tempered representations, which includes the Steinberg representation, and show that the restrictions of them are projective.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this paper we prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad.	result 0.88	0.96	0.97	asserted 1.00
s1	In particular, this implies a conjectural Euler--Poincar\'e characteristic formula for Gan--Gross--Prasad models.	interpretation 0.95	0.62	0.08	asserted 0.72
s2	Besides, we also single out a special class of tempered representations, which includes the Steinberg representation, and show that the restrictions of them are projective.	result 0.87	0.96	0.06	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 prove that Ext-analogues of Gan--Gross--Prasad models vanish for tempered representations, as conjectured by D. Prasad. In particular, this implies a conjectural Euler--Poincar\'e characteristic formula for Gan--Gross--Prasad models. Besides, we also single out a special class of tempered representations, which includes the Steinberg representation, and show that the restrictions of them are projective.

Human review

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

How the literature uses it

1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it

Cites it as background 1 paper

In other contexts, there are some recent progresses on the $$-vanishing results, see [ref] by Chan for the Rankin-Selberg case, [ref] by Cai and Fan for the triple product case, and [ref] by Chen for the Gan-Gross-Prasad case.

Ext-distinction for $p$-adic symmetric spaces · The linear case · 0.87

What it cites · 1 sentence without a confident label

Cites as background 2 papers

Readers may consult to [ref] , [ref] , [ref] , [ref] and [ref] for more details.

Endoscopic Classification of Representations: Inner Forms of Unitary Groups · Local Langlands correspondence · 1.00
Readers may consult to [ref] , [ref] , [ref] , [ref] and [ref] for more details.

Local Langlands Correspondence for Even Orthogonal Groups via Theta Lifts · Local Langlands correspondence · 1.00

Discussion

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