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- W2592530723 abstract "In recent work, Beukers characterized <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>{A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-hypergeometric systems having a full set of algebraic solutions. He accomplished this by (1) determining which <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>A</mml:mi> </mml:mrow> <mml:annotation encoding=application/x-tex>{A}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-hypergeometric systems have a full set of polynomial solutions modulo <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> for almost all primes <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=p> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=application/x-tex>p</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and (2) showing that these systems come from geometry. He then applied a fundamental theorem of N. Katz, which says that such systems have a full set of algebraic solutions. In this paper we establish some connections between nonresonant <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-hypergeometric systems and de Rham-type complexes, which leads to a determination of which <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-hypergeometric systems come from geometry. We do not use the fact that the system is irreducible or find integral formulas for its solutions." @default.
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- W2592530723 date "2011-10-13" @default.
- W2592530723 modified "2023-10-14" @default.
- W2592530723 title "𝐴-hypergeometric systems that come from geometry" @default.
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- W2592530723 doi "https://doi.org/10.1090/s0002-9939-2011-11073-6" @default.
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