On the p-adic L-function of a modular form at a supersingular prime

By Robert H. Pollack. 2003

175 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c13a3d8640748c9361f43038ebd932945a27abca

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Citations in the corpus

Wach modules and Iwasawa theory for modular forms (2009, unknown): “nd hence Kato’s) main conjecture can therefore not be translated into a statement relating L˜ p,αand Selp(f/Q∞) as in the ordinary case. When ap= 0, a remedy was made possible by the works of Pollack [Pol03]. If α1 and α2 are the roots of X2 +ǫ(p)pk−1, Pollack showed that there is a decomposition L˜”
Iwasawa theory of elliptic curves at supersingular primes over ℤ p -extensions of number fields (2004, methodology): “cal result assumes that we are working over Qp). For such K and p, we analyze arbitrary Zp-extensions of K. Following [13], we produce algebraic p-adic L-functions and then using the ideas of [8] and [17] we form plus/minus L-functions that actually lie in the Iwasawa algebra (assuming ap = 0). Atta”
The main conjecture for CM elliptic curves at supersingular primes (2005, background): “As is well known, it follows that p remains prime in K .I talso follows that ap = p +1 −| E(Fp)| =0 ,s ow ecan apply the results of the first author [ Po ] and Kobayashi [Ko].”
On anticyclotomic μ-invariants of modular forms (2006, background): “Under the assumption that ap = 0, two p-adic L-functions Lp (K∞, f), L − p (K∞, f) ∈ O[[Γ]] are constructed in [10] (in an analogous way to the cyclotomic construction of [26]).”
Iwasawa theory for modular forms at supersingular primes (2009, background): “If ∆ denotes the torsion subgroup of G∞ and γ is a fixed topological generator of the Zp-part of G∞, then Λ(G∞)∼= Zp[∆][[γ − 1]].”
Coleman maps and the p-adic regulator (2010, result): “This generalises the results of [Pollack 2003] (when ap = 0) and [Sprung 2009] (when f corresponds to an elliptic curve over Q and p = 3).”
Iwasawa theory for elliptic curves at supersingular primes (2003, background): “If η is trivial, we simply write L ± p (E, X ) for L ± p (E ,η ,X ). We remark that our sign of Pollack’s p-adic L-function is opposite to that in [ 18 ].”
Critical p-adic L-functions (2012, background): “[ PO ]) in the case where the coecient ap of the modular”