In mathematics, a Picard modular group, studied by Picard (1881), is a group of the form SU(J,L), where L is a 3-dimensional lattice over the ring of integers...

-É. Picard. Vol. I–IV. Paris: Centre National de la Recherche Scientifique. OCLC 4615520. Émile Picard Medal Picard modular group Picard modular surface...

a Picard modular surface, studied by Picard (1881), is a complex surface constructed as a quotient of the unit ball in C2 by a Picard modular group. Picard...

{\displaystyle \mathbb {C} } . An important example of this type of group is the Picard modular group SU ⁡ ( 2 , 1 ; Z [ i ] ) {\displaystyle \operatorname {SU}...

performed with unitary groups of hermitian forms, a well-known example is the Picard modular group. When G {\displaystyle G} is a Lie group one can define an...

is the upper half-plane and Γ {\displaystyle \Gamma } is the modular group. The Picard–Fuchs equation is then d 2 y d j 2 + 1 j d y d j + 31 j − 4 144...

of this surface into a projective space. Hilbert modular form Picard modular surface Siegel modular variety Ihara, Yasutaka; Nakamura, Hiroaki (1997)...

Felix Klein's j-invariant or j function is a modular function of weight zero for the special linear group SL ⁡ ( 2 , Z ) {\displaystyle \operatorname {SL}...

of the congruence group Γ(2), and generates the function field of the corresponding quotient, i.e., it is a Hauptmodul for the modular curve X(2). Over...

of a Fuchsian group, the others following as theorems. The notion of an invariant proper subset Δ is important; the so-called Picard group PSL(2,Z[i]) is...

class Serre's multiplicity conjectures Albanese variety Picard group Modular form Moduli space Modular equation J-invariant Algebraic function Algebraic form...

the Picard scheme (at any point) is equal to h 0 , 1 {\displaystyle h^{0,1}} . In characteristic 0 a result of Pierre Cartier showed that all groups schemes...

discontinuous (discrete group) theory was built up by Klein, Lie, Henri Poincaré, and Charles Émile Picard, in connection in particular with modular forms and monodromy...

elliptic modular surface of level 4 (the universal generalized elliptic curve E(4) → X(4)) in characteristic 3 mod 4 is a K3 surface with Picard number...

analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined...

I. Coornaert, Delzant & Papadopoulos 1990. For example, class groups and Picard groups; see Neukirch 1999, in particular §§I.12 and I.13 Seress 1997....

single-valued automorphic function for that triangle's triangle group. More specifically, it is a modular function. Let πα, πβ, and πγ be the interior angles at...

lemmas for U(3) and related groups", in Langlands, Robert P.; Ramakrishnan, Dinakar (eds.), The zeta functions of Picard modular surfaces, Montreal, QC: Univ...

that are also Shimura varieties: Hilbert modular surfaces Humbert surfaces Picard modular surfaces Shioda modular surfaces Elliptic surfaces, surfaces with...

groups of Lie type; with Michael Rapoport, Deligne worked on the moduli spaces from the 'fine' arithmetic point of view, with application to modular forms...

continuous groups, to complement the theory of discrete groups that had developed in the theory of modular forms, in the hands of Felix Klein and Henri Poincaré...

points on a Shimura variety modulo a prime of good reduction in The zeta functions of Picard modular surfaces, Publications du CRM, 1992, pp. 151-253....

known as the modularity theorem, and opened up entire new approaches to numerous other problems and mathematically powerful modularity lifting techniques...

stack of elliptic curves Moduli spaces of K-stable Fano varieties Modular curve Picard functor Moduli of semistable sheaves on a curve Kontsevich moduli...

ISBN 0-387-90108-6, MR 0396773 Kolchin, E. R. (1948), "Algebraic matric groups and the Picard–Vessiot theory of homogeneous linear ordinary differential equations"...

(the connected components of zero in Picard varieties) and Albanese varieties of other algebraic varieties. The group law of an abelian variety is necessarily...

are described by differential equations; the best-known of these is the Picard–Fuchs equation, which arises when the family of varieties is taken to be...

\operatorname {Div} ^{0}(E').} Alternatively, we can use the smaller Picard group Pic 0 {\displaystyle \operatorname {Pic} ^{0}} , a quotient of Div 0...

Groupe de Picard, anneaux factoriels, d'après Grothendieck (Picard group, unique factorisation domains) Alain Guichardet, Représentations des groupes de Lie...

be possible to construct a moduli stack. Mumford (1965) studied the Picard group of the moduli stack of elliptic curves, before stacks had been defined...