S. ANNI, A local-global principle for isogenies of prime degree over number fields, J. Lond. Math. Soc. (2) 89 (2014), no. 3, 745–761. https://dx.doi.org/10.1112/jlms/ jdu002. MR3217647.
G. BANASZAK AND K.S. KEDLAYA, An algebraic Sato-Tate group and Sato-Tate conjecture, Indiana Univ. Math. J. 64 (2015), no. 1, 245–274. https://dx.doi.org/10.1512/iumj.2015.64.5438. MR3320526.
B.S. BANWAIT, Examples of abelian surfaces failing the local-global principle for isogenies, Res. Number Theory 7 (2021), no. 3, Paper No. 55, 16 pp. https://dx.doi.org/10.1007/s40993-021-00283-9. MR4301391.
C. CHEVALLEY, Théorie des groupes de Lie. Tome III: Théorèmes généraux sur les algèbres de Lie, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], vol. No. 1226, Hermann & Cie, Paris, 1955 (French). MR0068552.
G. FALTINGS, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73 (1983), no. 3, 349–366 (German). https://dx.doi.org/10.1007/BF01388432. MR0718935.
F FITÉ, Artin representations attached to pairs of isogenous abelian varieties, J. Number Theory 133 (2013), no. 4, 1331–1345. https://dx.doi.org/10.1016/j.jnt.2012.09. 006. MR3004003.
F. FITÉ, On a local-global principle for quadratic twists of abelian varieties, Math. Ann. 388 (2024), no. 1, 769–794. https://dx.doi.org/10.1007/s00208-022-02535-0. MR4693946.
F. FITÉ AND X GUITART, Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of GL2-type, Math. Z. 300 (2022), no. 3, 2975–2995. https://dx.doi.org/10.1007/s00209-021-02895-4. MR4381226.
F. FITÉ, K.S. KEDLAYA, V. ROTGER, AND A.V. SUTHERLAND, Sato-Tate distributions and Galois endomorphism modules in genus 2, Compos. Math. 148 (2012), no. 5, 1390–1442. https://dx.doi.org/10.1112/S0010437X12000279. MR2982436.
THE GAP GROUP, GAP-Groups, Algorithms, and Programming, 2020, version 4.11.0, available at https://www.gap-system.org.
C.B. KHARE AND M. LARSEN, Abelian varieties with isogenous reductions, C. R. Math. Acad. Sci. Paris 358 (2020), no. 9–10, 1085–1089 (English, with English and French summaries). https://dx.doi.org/10.5802/crmath.129. MR4196779.
THE LMFDB COLLABORATION, The L-functions and Modular Forms Database, Online; accessed 12 September 2022, available at https://www.lmfdb.org.
D. LOMBARDO AND M. VERZOBIO, On the local-global principle for isogenies of abelian surfaces, Selecta Math. (N.S.) 30 (2024), no. 2, Paper no. 18, 68 pp. https://dx.doi.org/10.1007/s00029-023-00908-0. MR4695874.
B. MAZUR, K. RUBIN, AND A. SILVERBERG, Twisting commutative algebraic groups, J. Algebra 314 (2007), no. 1, 419–438. https://dx.doi.org/10.1016/j.jalgebra.2007.02.052. MR2331769.
J.S. MILNE, On the arithmetic of abelian varieties, Invent. Math. 17 (1972), 177–190. https://dx.doi.org/10.1007/BF01425446. MR0330174.
R. PINK, ℓ-adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture, J. Reine Angew. Math. 495 (1998), 187–237. https://dx.doi.org/10.1515/crll.1998.018. MR1603865.
C.S. RAJAN, On strong multiplicity one for ℓ-adic representations, Internat. Math. Res. Notices 3 (1998), 161–172. https://dx.doi.org/10.1155/S1073792898000142. MR1606395.
D. RAMAKRISHNAN, Recovering modular forms from squares, Invent. Math. 139 (2000), no. 1, 1–39, appendix to “A problem of Linnik for elliptic curves and mean-value estimates for automorphic representations” by W. Duke and E. Kowalski. https://dx.doi.org/10.1007/s002229900017. MR1728875.
K.A. RIBET, Galois action on division points of Abelian varieties with real multiplications, Amer. J. Math. 98 (1976), no. 3, 751–804. https://dx.doi.org/10.2307/2373815. MR0457455.
W.F. SAWIN, Ordinary primes for Abelian surfaces, C. R. Math. Acad. Sci. Paris 354 (2016), no. 6, 566–568 (English, with English and French summaries). https://dx.doi.org/10.1016/j.crma.2016.01.025. MR3494322.
J.-P. SERRE, Lectures on NX(p), Chapman & Hall/CRC Research Notes in Mathematics, vol. 11, CRC Press, Boca Raton, FL, 2012. MR2920749.
G. SHIMURA, Abelian Varieties with Complex Multiplication and Modular Functions, Princeton Mathematical Series, vol. 46, Princeton University Press, Princeton, NJ, 1998. https://dx.doi.org/10.1515/9781400883943. MR1492449.
A.V. SUTHERLAND, A local-global principle for rational isogenies of prime degree, J. Théor. Nombres Bordeaux 24 (2012), no. 2, 475–485 (English, with English and French summaries). http://dx.doi.org/10.5802/jtnb.807. MR2950703.
J. TATE, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134–144. https://dx.doi.org/10.1007/BF01404549. MR0206004.
I. VOGT, A local-global principle for isogenies of composite degree, Proc. Lond. Math. Soc. (3) 121 (2020), no. 6, 1496–1530. https://dx.doi.org/10.1112/plms.12378. MR4144369.
