Stratifications of flag spaces and functoriality

Goldring, Wushi; Koskivirta, Jean-Stefan

doi:10.48550/arxiv.1608.01504

Cited by 4 publications

(22 citation statements)

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“…By contrast, the connection with the EO stratification of Shimura varieties, also recalled below, gives particularly rich and special examples of G-Zips and is fruitful for applications to automorphic forms (cf. our previous papers [5,6]).…”

Section: Introductionmentioning

confidence: 99%

“…One of the key aims of this paper is to provide evidence to the contrary. The previous papers [12,11,5,6] already deduced nontrivial information about the global geometry of X from a study of group-theoretical Hasse invariants on G-Zip Z (and the closely related stacks of zip flags). For example, we showed by this method that the EO stratification of X is uniformly principally pure [5,Cor.…”

Section: Introductionmentioning

confidence: 99%

“…This note is concerned with an example where some global geometry of X may be understood purely in terms of X : the question of which automorphic vector bundles V X (λ) admit global sections on X. Our forthcoming joint work with Stroh and Brunebarbe [3] will study the closely related question of which V X (λ) are ample on X and on its partial flag spaces (see §1.3 below and [6]).…”

Section: Introductionmentioning

confidence: 99%

“…1.3. Review of flag spaces and their stratification ( [5,6]). Let (B, T ) be an F p -Borel pair of G such that B ⊂ P (this can be assumed after possibly conjugating…”

Section: Introductionmentioning

confidence: 99%

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Automorphic vector bundles with global sections on -schemes

Goldring¹,

Koskivirta²

2018

Compositio Math.

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A general conjecture is stated on the cone of automorphic vector bundles admitting nonzero global sections on schemes endowed with a smooth, surjective morphism to a stack of G-zips of connected-Hodge-type; such schemes should include all Hodge-type Shimura varieties with hyperspecial level. We prove our conjecture for groups of type A n 1 , C 2 , and Fp-split groups of type A 2 (this includes all Hilbert-Blumenthal varieties and should also apply to Siegel modular threefolds and Picard modular surfaces). An example is given to show that our conjecture can fail for zip data not of connected-Hodge-type.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…1.3. Review of flag spaces and their stratification ( [5,6]). Let (B, T ) be an F p -Borel pair of G such that B ⊂ P (this can be assumed after possibly conjugating…”

Section: Introductionmentioning

confidence: 99%

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Automorphic vector bundles with global sections on -schemes

Goldring¹,

Koskivirta²

2018

Compositio Math.

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“…This paper is the fourth installment in a series on our program to connect the three areas (A) Automorphic Algebraicity, (B) G-Zip-Geometricity and (C) Griffiths-Schmid Algebraicity. Our program was introduced in [13] and developed further in [14,12]. For more advances in the program, see our forthcoming joint work with Stroh and Brunebarbe [3].…”

Section: Introductionmentioning

confidence: 99%

Quasi-constant characters: Motivation, classification and applications

Goldring

Koskivirta

2018

Advances in Mathematics

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In [13], initially motivated by questions about the Hodge line bundle of a Hodge-type Shimura variety, we singled out a generalization of the notion of minuscule character which we termed quasi-constant. Here we prove that the character of the Hodge line bundle is always quasi-constant. Furthermore, we classify the quasi-constant characters of an arbitrary connected, reductive group over an arbitrary field. As an application, we observe that, if µ is a quasi-constant cocharacter of an Fp-group G, then our construction of group-theoretical Hasse invariants in loc. cit. applies to the stack G-Zip µ , without any restrictions on p, even if the pair (G, µ) is not of Hodge type and even if µ is not minuscule. We conclude with a more speculative discussion of some further motivation for considering quasi-constant cocharacters in the setting of our program outlined in loc. cit.

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Automorphic Forms on the Stack of G-Zips

Koskivirta

2019

Results Math

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We define automorphic vector bundles on the stack of G-zips introduced by Moonen-Pink-Wedhorn-Ziegler and study their global sections. In particular, we give a combinatorial condition on the weight for the existence of nonzero mod p automorphic forms on Shimura varieties of Hodge-type. We attach to the highest weight of the representation V (λ) a mod p automorphic form and we give a modular interpretation of this form in some cases.

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Stratifications of flag spaces and functoriality

Cited by 4 publications

References 0 publications

Automorphic vector bundles with global sections on -schemes

Automorphic vector bundles with global sections on -schemes

Quasi-constant characters: Motivation, classification and applications

Automorphic Forms on the Stack of G-Zips

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