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A quasicoherent sheaf . . .
, 2010
"... These are a bunch of notes taken to help myself learn algebraic geometry. My main sources are Harsthorne, FAC, and EGA. The organization is very much like EGA 0, since that’s kind of where I started. The notes ..."
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These are a bunch of notes taken to help myself learn algebraic geometry. My main sources are Harsthorne, FAC, and EGA. The organization is very much like EGA 0, since that’s kind of where I started. The notes
SUBSHEAVES OF A HERMITIAN TORSION FREE COHERENT SHEAF ON AN ARITHMETIC VARIETY
, 2006
"... Let K be a number field and OK the ring of integers of K. Let (E, h) be a hermitian finitely generated flat OKmodule. For an OKsubmodule F of E, let us denote by hF֒→E the submetric of F induced by h. It is well known that the set of all saturated OKsubmodules F with ̂ deg(F, hF֒→E) ≥ c is finit ..."
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Cited by 2 (0 self)
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Let K be a number field and OK the ring of integers of K. Let (E, h) be a hermitian finitely generated flat OKmodule. For an OKsubmodule F of E, let us denote by hF֒→E the submetric of F induced by h. It is well known that the set of all saturated OKsubmodules F with ̂ deg(F, hF֒→E) ≥ c is finite for any real
Sheaf Cohomology
, 2003
"... In this lecture, we define the cohomology groups of a topological space X with coefficients in a sheaf of abelian groups F on X in terms of the derived functors of the global section functor Γ(X, ·). Then we introduce Čech cohomology with respect to an open covering of X, which permits to make expl ..."
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In this lecture, we define the cohomology groups of a topological space X with coefficients in a sheaf of abelian groups F on X in terms of the derived functors of the global section functor Γ(X, ·). Then we introduce Čech cohomology with respect to an open covering of X, which permits to make
ON THE ISOMORPHISM BETWEEN THE DUALIZING SHEAF AND THE CANONICAL SHEAF
"... Abstract. We give a new proof of the isomorphism between the dualizing sheaf and the canonical sheaf of a nonsingular projective variety X over a perfect eld k. Our proof uses concepts and results from algebraic number theory. 1. ..."
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Abstract. We give a new proof of the isomorphism between the dualizing sheaf and the canonical sheaf of a nonsingular projective variety X over a perfect eld k. Our proof uses concepts and results from algebraic number theory. 1.
SHEAF REPRESENTATION OF NORMED SPACES
"... Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding to the cohe ..."
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Abstract. A multisorted limtheory, which has as Setvalued models all normed spaces over some specified fields, is introduced. We show that coherent extensions of this limtheory are expressive enough to characterise, for example, the Lpspaces. The sheafvalued spectra, corresponding
ON THE MODULI SPACE OF THE SCHWARZENBERGER BUNDLES
, 2002
"... For any odd n, we prove that the coherent sheaf FA on, defined as the cokernel of an injective map f: O⊕2 ..."
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Cited by 3 (1 self)
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For any odd n, we prove that the coherent sheaf FA on, defined as the cokernel of an injective map f: O⊕2
Sheaf Representation for Topoi
, 1997
"... It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of socalled hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of wellpointed topoi. Completeness ..."
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Cited by 4 (1 self)
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It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of socalled hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of wellpointed topoi. Completeness
Sheaf cohomology and free resolutions over the exterior algebras
, 2003
"... We derive an explicit version of the BernsteinGel’fandGel’fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free resolutions over its “Koszul dual ” exterior algebra. Among the facts about the BGG correspondence that we derive ..."
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Cited by 75 (20 self)
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We derive an explicit version of the BernsteinGel’fandGel’fand (BGG) correspondence between bounded complexes of coherent sheaves on projective space and minimal doubly infinite free resolutions over its “Koszul dual ” exterior algebra. Among the facts about the BGG correspondence that we
Cohomology of Coherent Sheaves and Series of Supernatural Bundles
, 2009
"... We show that the cohomology table of any coherent sheaf on projective space is a convergent—but possibly infinite—sum of positive real multiples of the cohomology tables of what we call supernatural sheaves. ..."
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Cited by 3 (2 self)
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We show that the cohomology table of any coherent sheaf on projective space is a convergent—but possibly infinite—sum of positive real multiples of the cohomology tables of what we call supernatural sheaves.
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