BibTex format
@unpublished{Pal:2020,
author = {Pal, A and Krishnamoorthy, R},
publisher = {arXiv},
title = {Rank 2 local systems and abelian varieties II},
url = {https://arxiv.org/abs/2003.07831v2},
year = {2020}
}
Publications
Citation
RIS format (EndNote, RefMan)
TY - UNPB
AB - LetX/Fq be a smooth, geometrically connected, quasi projective scheme. Let Ebe a semisimple over convergent F-isocrystal on X. Suppose that irreducible summands Ei of E have rank 2, determinant Qp (−1), and infinite monodromy at∞. Suppose further that for each closed point x of X, the characteristic polynomial of E at x is in Q[t]⊂Qp[t]. Then there exists a non-trivial open set U⊂X such that E|U comes from a family of abelian varieties on U. As an application, let L1 be an irreducible lisse Ql sheaf on X that has rank 2, determinant Ql(−1), and infinite monodromy at∞. Then all crystalline companions to L1 exist (as predicted by Deligne’s crystalline companions conjecture) if and only if there exists a non-trivial open set U⊂X and an abelian scheme πU: AU→U such that L1|U is a summand of R1(πU)∗ Ql.
AU - Pal,A
AU - Krishnamoorthy,R
PB - arXiv
PY - 2020///
TI - Rank 2 local systems and abelian varieties II
UR - https://arxiv.org/abs/2003.07831v2
UR - http://hdl.handle.net/10044/1/81866
ER -