Eigencurve

In number theory, an eigencurve is a rigid analytic curve that parametrizes certain p-adic families of modular forms, and an eigenvariety is a higher-dimensional generalization of this. Eigencurves were introduced by Coleman and Mazur (1998), and the term "eigenvariety" seems to have been introduced around 2001 by Kevin Buzzard (2007).

References

• Buzzard, Kevin (2007), "Eigenvarieties", in Burns, David; Buzzard, Kevin; Nekovář, Jan, L-functions and Galois representations, London Math. Soc. Lecture Note Ser., 320, Cambridge University Press, pp. 59–120, doi:10.1017/CBO9780511721267.004, ISBN 978-0-521-69415-5, https://www.ma.ic.ac.uk/~buzzard/maths/research/papers/eigenvarieties.pdf 
• Coleman, R.; Mazur, Barry (1998), "The eigencurve", Galois representations in arithmetic algebraic geometry (Durham, 1996), London Math. Soc. Lecture Note Ser., 254, Cambridge University Press, pp. 1–113, doi:10.1017/CBO9780511662010.003, ISBN 9780511662010