Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms

Iovită, Adrian; Spiess, Michael

doi:10.1007/s00222-003-0306-7

Cited by 33 publications

(74 citation statements)

References 23 publications

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“…Definition. We begin by recalling some generalities on Chow motives, following mainly [IS03,§5]. Let F be a field of characteristic zero, and S a smooth quasi-projective connected variety over F .…”

Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

“…Let F be an unramified field extension of Q p . For a semistable representation of G F = Gal(F /F ), let D st,F denote the semistable Dieudonné functor over F (see [IS03,§2]); so if V is a semistable representation of G F , then D st,F (V ) is a filtered Frobenius monodromy module over F (see [IS03,§2]); the category of such objects is denoted MF φ,N F , and for an object D in this category we denote F • (D) its filtration. For an object D in MF φ,N F , define (4)…”

Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

“…Let A e ⊂ H p be the oriented annulus in H p corresponding to e and U v ⊂ H p be the affinoid corresponding to v ∈ V, which are obtained as inverse images of the reduction map (see [IS03, page 342]). Recall that H 1 dR (X Γ , V n ) can be identified with theQ unr p -vector space of V n -valued, Γ-invariant differential forms of the second kind on H p modulo exact forms ([IS03, page 348]).…”

Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

“…where now Ext 1 MF φ,N Fv (·, ·) denotes the first Ext functor in the category MF φ,N Fv ([IS03, (44)]), and for an object M in this category, M [i] is its i-th fold twist described in [IS03,§2]. By [IS03, Lemma 2.1],…”

Section: 2mentioning

confidence: 99%

“…It turns out that our motive seems to be more flexible than the motive considered in [Mas12], and more natural because both the universal abelian variety and the fixed abelian variety with CM are false elliptic curves. In this context we define generalised Heegner cycles, and we study them using techniques from [IS03] and [BDP13].…”

Section: Introductionmentioning

confidence: 99%

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Generalized Heegner cycles on Mumford curves

Longo

Pati

2020

Math. Z.

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We study generalised Heegner cycles, originally introduced by Bertolini-Darmon-Prasanna for modular curves in [BDP13], in the context of Mumford curves. The main result of this paper relates generalized Heegner cycles with the two variable anticyclotomic p-adic L-function attached to a Coleman family f∞ and an imaginary quadratic field K, constructed in [BD07] and [Sev14]. While in [BD07] and [Sev14] only the restriction to the central critical line of this 2 variable p-adic L-function is considered, our generalised Heegner cycles allow us to study the restriction of this function to non-central critical lines. The main result expresses the derivative along the weight variable of this anticyclotomic p-adic L-function restricted to non necesserely central critical lines as a combination of the image of generalized Heegner cycles under a p-adic Abel-Jacobi map. In studying generalised Heegner cycles in the context of Mumford curves, we also obtain an extension of a result of Masdeu [Mas12] for the (one variable) anticyclotomic p-adic L-function of a modular form f and K at non-central critical integers.

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Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

Section: The Generalised Kuga-sato Motivementioning

confidence: 99%

Section: 2mentioning

confidence: 99%