Modular symbols for reductive groups and p-adic Rankin–Selberg convolutions over number fields

Januszewski, Fabian

doi:10.1515/crelle.2011.018

Cited by 24 publications

(39 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For n = 1 this recovers the classical "modular symbol" construction of norm-compatible families of classes in Betti H 1 of modular curves, given by paths between cusps, and thus we recover the classical construction of the standard p-adic L-function of a modular form. For n > 1, we obtain p-adic L-functions associated to Rankin-Selberg L-functions for GL n × GL n+1 ; this recovers a construction due to Kazhdan-Mazur-Schmidt [17] and Januszewski [14].…”

Section: Diagonal Embeddings Of General Linear Groupssupporting

confidence: 65%

Spherical varieties and norm relations in Iwasawa theory

Loeffler¹

2022

Journal De Théorie Des Nombres De Bordeaux

View full text Add to dashboard Cite

L'accès aux articles de la revue « Journal de Théorie des Nombres de Bordeaux » (http://jtnb.centre-mersenne.org/), implique l'accord avec les conditions générales d'utilisation (http://jtnb. centre-mersenne.org/legal/). Toute reproduction en tout ou partie de cet article sous quelque forme que ce soit pour tout usage autre que l'utilisation à fin strictement personnelle du copiste est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. cedramArticle mis en ligne dans le cadre du Centre de diffusion des revues académiques de mathématiques http://www.centre-mersenne.org/

show abstract

Section: Diagonal Embeddings Of General Linear Groupssupporting

confidence: 65%

Spherical varieties and norm relations in Iwasawa theory

Loeffler¹

2022

Journal De Théorie Des Nombres De Bordeaux

View full text Add to dashboard Cite

show abstract

“…In order to have a hope of executing this strategy it is crucial to have algebraicity results for critical L-values of π based upon period integrals over a group H ⊂ G, which do not involve an Eisenstein series; for example, in the case of G = GL n × GL n−1 , where critical L-values can be computed from diagonally embedding H = GL n−1 . One should then be able to construct evaluation maps based on cycles obtained from H, and via the overconvergent cohomology approach, be able to recover/generalise results of Januszewski [Jan11,Jan15].…”

Section: I4 Bottom Row: Classical Computationsmentioning

confidence: 99%

Parabolic eigenvarieties via overconvergent cohomology

Salazar¹,

Williams²

2021

Math. Z.

View full text Add to dashboard Cite

Let $$\mathcal {G}$$ G be a connected reductive group over $$\mathbf {Q}$$ Q such that $$G = \mathcal {G}/\mathbf {Q}_p$$ G = G / Q p is quasi-split, and let $$Q \subset G$$ Q ⊂ G be a parabolic subgroup. We introduce parahoric overconvergent cohomology groups with respect to Q, and prove a classicality theorem showing that the small slope parts of these groups coincide with those of classical cohomology. This allows the use of overconvergent cohomology at parahoric, rather than Iwahoric, level, and provides flexible lifting theorems that appear to be particularly well-adapted to arithmetic applications. When Q is a Borel, we recover the usual theory of overconvergent cohomology, and our classicality theorem gives a stronger slope bound than in the existing literature. We use our theory to construct Q-parabolic eigenvarieties, which parametrise p-adic families of systems of Hecke eigenvalues that are finite slope at Q, but that allow infinite slope away from Q.

show abstract

“…In the literature, many theorems on special values of L-functions have been proved under the assumption that Theorem A is valid. See Kazhdan-Mazur-Schmidt [KMS], Mahnkopf [Mah], Raghuram [Rag1], Kasten-Schmidt [KS], Januszewski [Jan1], RS2], and Schmidt [Sch1,Sch2]. For more recent works using Theorem A (and Theorem C of Section 6), see Grobner-Harris [GH], Raghuram [Rag2], and Januszewski [Jan2,Jan3,Jan4].…”

Section: Introductionmentioning

confidence: 99%