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    On the Denjoy-Carleman-Ahlfors Theorem
    Annals of Mathematics (1948)
    Maurice Heins
    Citations (10)
    A sharp form of Nevanlinna’s second main theorem of several complex variables
    Mathematische Zeitschrift (1996)
    Zhuan Ye
    Several complex variables
    Nevanlinna Theory
    Citations (13)
    Negative definite functions on commutative hypergroups
    Lecture notes in mathematics (1989)
    Michael Voit
    Citations (8)
    Surjectivity of multifunctions under generalized differentiability assumptions
    Bulletin of the Australian Mathematical Society (1983)
    Serge GautierG. IsacJean‐Paul Penot
    The aim of the present paper is to give some general surjectivity theorems for multifunctions using tangent cones and generalized differentiability assumptions.
    Tangent cone
    Citations (7)
    An existence theorem for a general Goursat problem
    Journal of Differential Equations (1969)
    Jan Persson
    Citations (5)
    Kennzeichnung derp-adischen und der endlichen algebraischen Zahlk�rper
    Inventiones mathematicae (1969)
    J�rgen Neukirch
    Citations (76)
    The $p$-adic Lefschetz $(1,1)$ theorem in the semistable case, and the Picard number jumping locus
    Mathematical Research Letters (2011)
    Go Yamashita
    We prove a semistable version of the so-called p-adic Lefschetz (1, 1) theorem.As an application, we show a generalization of the Maulik-Poonen result on Picard number jumping locus. Introduction.Let K be a complete discrete valuation field of mixed characteristic (0, p) whose residue field k is perfect.Let X be a proper semistable model over S := Spec O K , X K be its generic fiber X ⊗ O K K, and Y be its special fiberwhere W is the ring of Witt vectors with coefficient k, and M Y and N 0 are logstructures on Y and Spec W respectively (the precise meaning of notations will be explained later).We also have Hyodo-Kato isomorphism ([HK])).This isomorphism depends on the choice of a uniformizer π ∈ K.However, we can show that ρ π (c crys ([L])) is independent of the choice of π (Corollary 2.3).In this paper, we first show the following generalization of the Berthelot-Ogus theorem ([BO, Theorem (3.8)]):Next, by using this theorem, we deduce a generalization of the Maulik-Poonen result ([MP]) (see Section 4 for precise meaning of the notations):
    Citations (6)
    On the Number of Subgroups of Index Two-An Application of Goursat's Theorem for Groups
    Mathematics Magazine (1975)
    R. R. CrawfordK. D. Wallace
    Citations (3)
    L(R) with determinacy satisfies the Suslin hypothesis
    Advances in Mathematics (2019)
    William ChanStephen Jackson
    Citations (6)
    Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma
    Tatra Mountains Mathematical Publications (2014)
    László Tóth
    Abstract Using Goursat’s lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z m × Z n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.
    Lemma (botany)
    Rank (graph theory)
    Citations (16)