Rigid analytic spaces with overconvergent structure sheaf

AbstractSuppose{({\mathscr{T}},\otimes,\mathds{1})}is a tensor triangulated category. In a number of recent articles Balmer defines and explores the notion of “separable tt-rings” in{{\mathscr{T}}}(in this paper we will call them “separable monoids”). The main result of this article is that, if{{\mathscr{T}}}is the derived quasicoherent category of a noetherian schemeX, then the only separable monoids are the pushforwards by étale maps of smashing Bousfield localizations of the structure sheaf.

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Analyticity of the Singular Locus. Normalization of the Structure Sheaf

Grundlehren der mathematischen Wissenschaften - Coherent Analytic Sheaves ◽

10.1007/978-3-642-69582-7_6 ◽

1984 ◽

pp. 113-129

Author(s):

Hans Grauert ◽

Reinhold Remmert

Keyword(s):

Singular Locus ◽

Structure Sheaf

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On the Frobenius direct image of the structure sheaf of a homogeneous projective variety

Journal of Algebra ◽

10.1016/j.jalgebra.2018.07.003 ◽

2018 ◽

Vol 512 ◽

pp. 160-188

Author(s):

Masaharu Kaneda

Keyword(s):

Projective Variety ◽

Direct Image ◽

Structure Sheaf

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A structure sheaf on noetherian rings

Communications in Algebra ◽

10.1080/00927879408825038 ◽

1994 ◽

Vol 22 (9) ◽

pp. 3511-3530

Author(s):

J.L. Bueso ◽

P. Jara ◽

L. Merino

Keyword(s):

Noetherian Rings ◽

Structure Sheaf

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Formality of -objects

Compositio Mathematica ◽

10.1112/s0010437x19007218 ◽

2019 ◽

Vol 155 (5) ◽

pp. 973-994

Author(s):

Andreas Hochenegger ◽

Andreas Krug

Keyword(s):

Projective Variety ◽

Smooth Projective Variety ◽

Complex Numbers ◽

Cohomology Algebra ◽

Triangulated Category ◽

Endomorphism Algebra ◽

Structure Sheaf

We show that a$\mathbb{P}$-object and simple configurations of$\mathbb{P}$-objects have a formal derived endomorphism algebra. Hence the triangulated category (classically) generated by such objects is independent of the ambient triangulated category. We also observe that the category generated by the structure sheaf of a smooth projective variety over the complex numbers only depends on its graded cohomology algebra.

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