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, and the term "eigenvariety" seems to have been introduced by Buzzard.

References

• Buzzard, Kevin (2007). "Eigenvarieties". In Burns, David; Buzzard, Kevin; Nekovář, Jan (eds.). L-Functions and Galois Representations. London Mathematical Society Lecture Note Series. Vol. 320. Cambridge University Press. pp. 59–120. doi:10.1017/CBO9780511721267.004. ISBN 978-0-521-69415-5. MR 2392353.

• Coleman, R.; Mazur, B. (1998). "The eigencurve". In Scholl, A. J.; Taylor, R. L. (eds.). Galois Representations in Arithmetic Algebraic Geometry. London Mathematical Society Lecture Note Series. Vol. 254. Cambridge University Press. pp. 1–113. doi:10.1017/CBO9780511662010.003. ISBN 0-521-64419-4. MR 1696469.