Quasi-constant characters: Motivation, classification and applications

Goldring, Wushi; Koskivirta, Jean-Stefan

doi:10.1016/j.aim.2018.09.026

Cited by 4 publications

(10 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the classical theory this amounts to the case that the VHS V is polarized of weight one. Here we recover the results of our joint work with Koskivirta [12]. The second example provides explicit formulas for grif(G, µ, r) when r = Ad is the adjoint representation, essentially in terms of the Coxeter number of the underlying root system.…”

Section: Introductionsupporting

confidence: 65%

See 1 more Smart Citation

The Griffiths bundle is generated by groups

Goldring

2019

Math. Ann.

Self Cite

View full text Add to dashboard Cite

First the Griffiths line bundle of a Q-VHS V is generalized to a Griffiths character grif(G, µ, r) associated to any triple (G, µ, r), where G is a connected reductive group over an arbitrary field F , µ ∈ X * (G) is a cocharacter (over F ) and r : G → GL(V ) is an F -representation; the classical bundle studied by Griffiths is recovered by taking F = Q, G the Mumford-Tate group of V , r : G → GL(V ) the tautological representation afforded by a very general fiber and pulling back along the period map the line bundle associated to grif(G, µ, r). The more general setting also gives rise to the Griffiths bundle in the analogous situation in characteristic p given by a scheme mapping to a stack of G-Zips.When G is F -simple, we show that, up to positive multiples, the Griffiths character grif(G, µ, r) (and thus also the Griffiths line bundle) is essentially independent of r with central kernel, and up to some identifications is given explicitly by −µ. As an application, we show that the Griffiths line bundle of a projective G-Zip µ -scheme is nef.

show abstract

Section: Introductionsupporting

confidence: 65%

“…The condition "orbitally p-close" is a weakening of certain p-smallness conditions, while "quasi-constant" generalizes "minuscule". See [12] for more on quasi-constant (co)characters.…”

Section: 44mentioning

confidence: 99%

The Griffiths bundle is generated by groups

Goldring

2019

Math. Ann.

Self Cite

View full text Add to dashboard Cite

show abstract

“…[38], Th.1.4.4). The Hodge character η ω of a symplectic embedding ϕ ′ : (G, X) ֒→ (GSp(2g), X g ) is quasi-constant (Def.…”

mentioning

confidence: 96%

Strata Hasse invariants, Hecke algebras and Galois representations

Goldring

Koskivirta

2019

Invent. math.

Self Cite

View full text Add to dashboard Cite

We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks G-Zip µ . Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags G-ZipFlag µ , fibered in flag varieties over G-Zip µ . It provides a simultaneous generalization of the "classical case" homogeneous complex manifolds studied by Griffiths-Schmid and the "flag space" for Siegel varieties studied by Ekedahl-van der Geer.Four applications are obtained: (1) Pseudo-representations are attached to the coherent cohomology of Hodgetype Shimura varieties modulo a prime power. (2) Galois representations are associated to many automorphic representations with non-degenerate limit of discrete series archimedean component. (3) It is shown that all Ekedahl-Oort strata in the minimal compactification of a Hodge-type Shimura variety are affine, thereby proving a conjecture of Oort. (4) Part of Serre's letter to Tate on mod p modular forms is generalized to general Hodge-type Shimura varieties.

show abstract

“…In [4], the authors classified quasi-constant (co)characters and showed that the notion 'quasi-constant' naturally unifies those of minuscule and co-minuscule. In particular, if k is algebraically closed and G is simple, then a character χ ∈ X * (T) is quasi-constant if and only if it is a multiple of a fundamental weight (relative some choice of simple roots ∆ ⊂ Φ) which is either minuscule or co-minuscule [4, Th.…”

mentioning

confidence: 99%

“…In [4], see esp. §5.2, we argued why it seemed that'quasi-constant' was perhaps a more natural notion than either 'minuscule' or 'co-minuscule' separately.…”

mentioning

confidence: 99%