Reviewed Articles

Anni, Samuele; Dokchitser, Vladimir, Constructing hyperelliptic curves with surjective Galois representations, Trans. Am. Math. Soc. 373, 1477-1500 (2020) 

Dąbrowski, Andrzej; Pomykała, Jacek, On a Linnik problem for elliptic curves, Proc. Am. Math. Soc. 147, 3759-3763 (2019) 

Gao, Ziyang, Generic rank of Betti map and unlikely intersections, Compos. Math. 156, 2469-2509 (2020) 

Costa, Edgar; Lombardo, Davide; Voight, John, Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms, Res. Number Theory 7, Paper No. 46, 14 p. (2021) 

Beshaj, Lubjana; Polak, M., On hyperelliptic curves of genus 3, Algebraic curves and their applications. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 724, 161-173 (2019). 

Bruin, Nils; Sertöz, Emre Can, Prym varieties of genus four curves, Trans. Am. Math. Soc. 373, 149-183 (2020). 

Rasmussen, Christopher; Tamagawa, Akio, Cyclic covers and Ihara's question, Res. Number Theory 5, Paper No. 33, 23 p. (2019). 

Böckle, Gebhard; Gajda, Wojciech; Petersen, Sebastian, A variational open image theorem in positive characteristic, J. Théor. Nombres Bordx. 30, 965-977 (2018). 

Carocca, Angel; Lange, Herbert; Rodríguez, Rubí E., Étale double covers of cyclic $p$-gonal covers, J. Algebra 538, 110-126 (2019). 

Zarhin, Yu. G., Division by 2 on odd-degree hyperelliptic curves and their Jacobians, Izv. Math. 83, No. 3, 501-520 (2019); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 83, No. 3, 93-112 (2019). 

Stoll, Michael, Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank, J. Eur. Math. Soc. (JEMS) 21, No. 3, 923-956 (2019) 

De Marco, Laura: Dynamical moduli spaces and elliptic curves, Ann. Fac. Sci. Toulouse, Math. (6) 27, No. 2, 389-420 (2018).

Krieger, Holly; Levin, Aaron; Scherr, Zachary; Tucker, Thomas; Yasufuku, Yu; Zieve, Michael E.: Uniform boundedness of $S$-units in arithmetic dynamics, Pac. J. Math. 274, No. 1, 97-106 (2015).

Agwu, Anthony; Harris, Phillip; James, Kevin; Kannan, Siddarth; Li, Huixi: Frobenius distributions in short intervals for CM elliptic curves, J. Number Theory 188, 263-280 (2018).

Im, Bo-Hae; Wallace, Erik: Rank gain of Jacobian varieties over finite Galois extensions, J. Number Theory 184, 68-84 (2018).

Liu, Yifeng: Hirzebruch-Zagier cycles and twisted triple product Selmer groups, Invent. Math. 205, No. 3, 693-780 (2016).

Kisin, Mark: Mod $p$ points on Shimura varieties of abelian type, J. Am. Math. Soc. 30, No. 3, 819-914 (2017).

Bhargava, Manjul; Gross, Benedict H.; Wang, Xiaoheng: A positive proportion of locally soluble hyperelliptic curves over $\mathbb {Q}$ have no point over any odd degree extension, J. Am. Math. Soc. 30, No. 2, 451-493 (2017).

Ishitsuka, Yasuhiro; Ito, Tetsushi: The local-global principle for symmetric determinantal representations of smooth plane curves in characteristic two, J. Pure Appl. Algebra 221, No. 6, 1316-1321 (2017).

Aubry, Yves; Haloui, Safia: On the number of rational points on Prym varieties over finite fields, Glasg. Math. J. 58, No. 1, 55-68 (2016).

Delbourgo, Daniel; Lei, Antonio: Transition formulae for ranks of abelian varieties, Rocky Mt. J. Math. 45, No. 6, 1807-1838 (2015).

Park, Seungkook: Hyperelliptic curves for the vector decomposition problem over fields of even characteristic, J. Appl. Math. 2015, Article ID 197097, 6 p. (2015).

Kani, Ernst: The moduli spaces of Jacobians isomorphic to a product of two elliptic curves, Collect. Math. 67, No. 1, 21-54 (2016).

Zarhin, Yuri G.: Two-dimensional families of hyperelliptic Jacobians with big monodromy, Trans. Am. Math. Soc. 368, No. 5, 3651-3672 (2016).

Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen: Explicit Galois obstruction and descent for hyperelliptic curves with tamely cyclic reduced automorphism group, Math. Comput. 85, No. 300, 2011-2045 (2016).

Chou, Michael: Torsion of rational elliptic curves over quartic Galois number fields, J. Number Theory 160, 603-628 (2016).

Lombardo, Davide: Bounds for Serre's open image theorem for elliptic curves over number fields, Algebra Number Theory 9, No. 10, 2347-2395 (2015).

de Jong, Robin: Local heights on Galois covers of the projective line, Acta Arith. 152, No. 1, 51-70 (2012).

Ghate, E.; Parent, P.: On uniform large Galois images for modular abelian varieties, Bull. Lond. Math. Soc. 44, No. 6, 1169-1181 (2012).

Haloui, Safia; Singh, Vijaykumar: The characteristic polynomials of abelian varieties of dimension 4 over finite fields, Aubry, Yves (ed.) et al., Arithmetic, geometry, cryptography and coding theory. 13th conference on arithmetic, geometry, cryptography and coding theory, CIRM, Marseille, France, March 14--18, 2011 and Geocrypt 2011, Bastia, France, June 19--24, 2011. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7572-8/pbk; 978-0-8218-9027-1/ebook). Contemporary Mathematics 574, 59-68 (2012).

Álvarez, A.: The p-rank of the reduction modp of Jacobians and Jacobi sums, Int. J. Number Theory 10, No. 8, 2097-2114 (2014).

Takagi, Toshikazu: The Q-rational cuspidal group of J 1 (2p), J. Math. Soc. Japan 66, No. 4, 1249-1301 (2014).

Fisher, Tom: Invisibility of Tate-Shafarevich groups in abelian surfaces, Int. Math. Res. Not. 2014, No. 15, 4085-4099 (2014).

von Känel, Rafael: On Szpiro’s discriminant conjecture, Int. Math. Res. Not. 2014, No. 16, 4457-4491 (2014)

González-Jiménez, Enrique; Xarles, Xavier: On a conjecture of Rudin on squares in arithmetic progressions, LMS J. Comput. Math. 17, 58-76, electronic only (2014).

Fité, Francesc; Sutherland, Andrew: Sato-Tate distributions of twists of y^2 =x^5 -x and y^2 =x^6 +1, Algebra Number Theory 8, No. 3, 543-585 (2014).

Cheng, Chuangxun: A relation between the Brauer group and the Tate-Shafarevich group, Comment. Math. 47, No. 2, 149-156 (2012).

Byeon, Dongho; Kim, Nayoung: Elliptic curves of rank zero satisfying the p-part of the Birch and Swinnerton-Dyer conjecture, Manuscr. Math. 142, No. 3-4, 383-390 (2013).

Sahinoglu, Hatice: On the independence of Heegner points on CM elliptic curves associated to distinct quadratic imaginary fields, Proc. Am. Math. Soc. 141, No. 3, 813-826 (2013).

Byeon, Dongho; Yhee, Donggeon: Optimal curves differing by a 3-isogeny, Acta Arith. 158, No. 3, 219-227 (2013).

Arias-de-Reyna, Sara; Gajda, Wojciech; Petersen, Sebastian: Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion, Math. Nachr. 286, No. 13, 1269-1286 (2013).

Poonen, Bjorn; Rains, Eric: Random maximal isotropic subspaces and Selmer groups, J. Am. Math. Soc. 25, No. 1, 245-269 (2012).

Gillibert, Jean; Wuthrich, Christian: The class group pairing and $p$-descent on elliptic curves, Proc. Lond. Math. Soc. (3) 106, No. 2, 345-374 (2013).

Onishi, Yoshihiro: Determinant formulae in abelian functions for a general trigonal curve of degree five, Comput. Methods Funct. Theory 11, No. 2, 547-574 (2011).

Im, Bo-Hae; Larsen, Michael: Parallelopipeds of positive rank twists of elliptic curves, Indiana Univ. Math. J. 60, No. 1, 311-318 (2011).

Guitart, Xavier: Abelian varieties with many endomorphisms and their absolutely simple factors, Rev. Mat. Iberoam. 28, No. 2, 591-601 (2012).

Siksek, Samir; Stoll, Michael: Partial descent on hyperelliptic curves and the generalized Fermat equation $x^3+y^4+z^5=0$, Bull. Lond. Math. Soc. 44, No. 1, 151-166 (2012).

Bilu, Yuri; Masser, David; Zannier, Umberto: An effective Theorem of Andre for CM-points on a plane curve, Math. Proc. Camb. Philos. Soc. 154, No. 1, 145-152 (2013).

Cremona, J.E.; Fisher, T.A.; O'Neil, C.; Simon, D.; Stoll, M.: Explicit $n$-descent on elliptic curves. II: Geometry, J. Reine Angew. Math. 632, 163-84 (2009).

Cremona, J.E.; Fisher, T.A.; O'Neil, C.; Simon, D.; Stoll, M.: Explicit $n$-descent on elliptic curves. I: Algebra, J. Reine Angew. Math. 615, 121-155 (2008).

Perucca, Antonella : Two variants of the support problem for products of abelian varieties and tori, J. Number Theory 129, 1883-1892 (2009).

N. Bruin, K. Doerksen : The arithmetic of genus two curves with (4,4)-split Jacobians, Canad. J. Math. 63, 992-1024 (2011).

A. Ashtaneh-Asl, H. Daghigh : Independence of Heegner points for nonmaximal orders, Int. J. Number Theory 7, 663-669 (2011).

Merel, L.: Normalizers of split Cartan subgroups and supersingular elliptic curves, Zannier, Umberto (ed.), Diophantine geometry. Selected papers of a the workshop, Pisa, Italy, April 12--July 22, 2005. Pisa: Edizioni della Normale. Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) 4, 237-255 (2007).

P. Jossen, A. Perucca: A counterexample to the local-global principle of linear dependence for Abelian varieties, C.R. Acad. Sci. Paris, Ser. I 348, 9-10 (2010)

F. Najman: Compack representation of quadratic integers and integer points on some elliptic curves, Rocky Mt. J. Math. 40 , 1979-2002 (2010)

D. Byeon, D. Yhee: Rational torsion on optimal curves and rank-one quadratic twists, J. Number Theory 131, 552-560 (2011)

Y. Bilu, M. Strambi: Quantitative Riemann Existence Theorem over a number field, Acta Arith. 145, 319-339 (2010)

E. Bombieri, P. Habegger, D. Masser, U. Zannier: A note on Maurin's theorem, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser., Rend. Lincei, Mat. Appl. 21, 251-260 (2010)

H. Chapdelaine: Non-abelian descent and the generalized Fermat equation, Clay Mathematics Proceedings 8, 55-69 (2009)

M. Volkov: Abelian surfaces with supersingular good reduction and non-semisimple Tate module, Int. J. Number Theory 6, 811-818 (2010)

A. Perucca: On the problem of detecting linear dependence for products of abelian varieites and tori, Acta. Arith. 142, 119--128 (2010).

A. Momot: On the classification of complex tori arising from real abelian surfaces, Abh. Math. Semin. Univ. Hamb. 79, 283-298 (2009).

H. Sakagawa: Study of group orders of elliptic curves, J. Math. Kyoto Univ. 48, No. 4 Article ID 2, 723-746 (2008).

Y. Zarhin: Families of absolutely simple hyperelliptic Jacobians, Proc. Lond. Math. Soc. (3) 100, No. 1, 24-54 (2010).

N. Bruin: The arithmetic of Prym varieties in genus 3, Compos. Math. 144, No. 2, 317-338 (2008).

D. Poulakis: On the rational points of the curve f(X,Y)q=h(X) g(X,Y), Can. Math. Bull. 52, No. 1, 117-126 (2009).

M. Stoll: Finite descent obstructions and rational points on curves, Algebra & Number Theory, No. 1, 349-391 (2007).

K. Miyake: Twists of Hessian elliptic curves and cubic fields, Ann. Math. Blaise Pascal 16, No. 1, 27-45 (2009).

E.V. Flynn: Homogeneous spaces and degree 4 del Pezzo surfaces, Manuscr. Math. 129, No. 3, 369-380 (2009).