Rank 2 local systems, Barsotti–Tate groups, and
Shimura curves

Krishnamoorthy, Raju

doi:10.2140/ant.2022.16.231

Cited by 1 publication

(6 citation statements)

References 23 publications

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“…We claim this process must terminate at some point. Here is a simple proof (also indicated in [Kri22,p. 253]).…”

Section: Drinfeld's Work On the Langlands Correspondence For Gl 2 And...mentioning

confidence: 94%

“…We claim this process must terminate at some point. Here is a simple proof (also indicated in [Kri22, p. 253]). Let be a closed point of such that is supersingular.…”

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 94%

“…Suppose further that is an irreducible object of . Then: is generically ordinary with a non-empty supersingular locus; and there exists an isogenous -divisible group that is generically versally deformed (in the sense of [Kri22, Defintions 8.1, 8.2]) 8 …”

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 99%

“…there exists an isogenous -divisible group that is generically versally deformed (in the sense of [Kri22, Defintions 8.1, 8.2]) 8…”

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 99%

“…When we do not assume infinite monodromy at , then no such result is known; more specifically, the output of his later work on the Langlands correspondence will imply that there exists an open subset and a smooth projective morphism of relative dimension 2 such that is a summand of . See [Kri22, Remark 1.4, Question 9.1] and [KP21, § 1] for related discussion.…”

Section: Introductionmentioning

confidence: 99%

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Constructing abelian varieties from rank 2 Galois representations

Krishnamoorthy,

Yang,

Zuo

2024

Compositio Math.

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Let $U$ be a smooth affine curve over a number field $K$ with a compactification $X$ and let ${\mathbb {L}}$ be a rank $2$ , geometrically irreducible lisse $\overline {{\mathbb {Q}}}_\ell$ -sheaf on $U$ with cyclotomic determinant that extends to an integral model, has Frobenius traces all in some fixed number field $E\subset \overline {\mathbb {Q}}_{\ell }$ , and has bad, infinite reduction at some closed point $x$ of $X\setminus U$ . We show that ${\mathbb {L}}$ occurs as a summand of the cohomology of a family of abelian varieties over $U$ . The argument follows the structure of the proof of a recent theorem of Snowden and Tsimerman, who show that when $E=\mathbb {Q}$ , then ${\mathbb {L}}$ is isomorphic to the cohomology of an elliptic curve $E_U\rightarrow U$ .

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“…We claim this process must terminate at some point. Here is a simple proof (also indicated in [Kri22,p. 253]).…”

Section: Drinfeld's Work On the Langlands Correspondence For Gl 2 And...mentioning

confidence: 94%

“…We claim this process must terminate at some point. Here is a simple proof (also indicated in [Kri22, p. 253]). Let be a closed point of such that is supersingular.…”

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 94%

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 99%

“…there exists an isogenous -divisible group that is generically versally deformed (in the sense of [Kri22, Defintions 8.1, 8.2]) 8…”

Section: Drinfeld's Work On the Langlands Correspondence For And Som...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Constructing abelian varieties from rank 2 Galois representations

Krishnamoorthy,

Yang,

Zuo

2024

Compositio Math.

Self Cite

View full text Add to dashboard Cite

show abstract

Rank 2 local systems, Barsotti–Tate groups, and Shimura curves

Cited by 1 publication

References 23 publications

Constructing abelian varieties from rank 2 Galois representations

Constructing abelian varieties from rank 2 Galois representations

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