Some Analogues of Hartogs' Theorem in an Algebraic Setting

1978 ◽  
Vol 100 (2) ◽  
pp. 387 ◽  
Author(s):  
Richard S. Palais
Keyword(s):  
Algebraic Setting ◽  
Hartogs Theorem

scholarly journals Goresky–Pardon lifts of Chern classes and associated Tate extensions

2017 ◽  
Vol 153 (7) ◽  
pp. 1349-1371 ◽  
Author(s):  
Eduard Looijenga
Keyword(s):  
Vector Bundle ◽  
Hodge Structure ◽  
Holomorphic Vector Bundle ◽  
Mixed Hodge Structure ◽  
Chern Classes ◽  
Analytic Variety ◽  
Algebraic Setting ◽  
Geometric Conditions ◽  
Stable Cohomology ◽  
Complex Analytic Variety

Let $X$ be an irreducible complex-analytic variety, ${\mathcal{S}}$ a stratification of $X$ and ${\mathcal{F}}$ a holomorphic vector bundle on the open stratum ${X\unicode[STIX]{x0030A}}$. We give geometric conditions on ${\mathcal{S}}$ and ${\mathcal{F}}$ that produce a natural lift of the Chern class $\operatorname{c}_{k}({\mathcal{F}})\in H^{2k}({X\unicode[STIX]{x0030A}};\mathbb{C})$ to $H^{2k}(X;\mathbb{C})$, which, in the algebraic setting, is of Hodge level ${\geqslant}k$. When applied to the Baily–Borel compactification $X$ of a locally symmetric variety ${X\unicode[STIX]{x0030A}}$ and an automorphic vector bundle ${\mathcal{F}}$ on ${X\unicode[STIX]{x0030A}}$, this refines a theorem of Goresky–Pardon. In passing we define a class of simplicial resolutions of the Baily–Borel compactification that can be used to define its mixed Hodge structure. We use this to show that the stable cohomology of the Satake ($=$ Baily–Borel) compactification of ${\mathcal{A}}_{g}$ contains nontrivial Tate extensions.

A linear algebraic setting for Jacobi structures

2021 ◽  
Vol 159 ◽  
pp. 103904
Author(s):  
Eugen-Mihăiţă Cioroianu ◽  
Cornelia Vizman
Keyword(s):  
Algebraic Setting

scholarly journals Expressibility of properties of relations

1995 ◽  
Vol 60 (3) ◽  
pp. 970-991 ◽  
Author(s):  
Hajnal Andréka ◽  
Ivo Düntsch ◽  
István Németi
Keyword(s):  
Algebraic Setting ◽  
Algebras Of Relations

AbstractWe investigate in an algebraic setting the question of which logical languages can express the properties integral, permutational, and rigid for algebras of relations.

scholarly journals QUANTUM HYPOTHESIS TESTING AND NON-EQUILIBRIUM STATISTICAL MECHANICS

2012 ◽  
Vol 24 (06) ◽  
pp. 1230002 ◽  
Author(s):  
V. JAKŠIĆ ◽  
Y. OGATA ◽  
C.-A. PILLET ◽  
R. SEIRINGER
Keyword(s):  
Statistical Mechanics ◽  
Hypothesis Testing ◽  
Large Deviation ◽  
Quantum Statistical Mechanics ◽  
Entropy Flow ◽  
Quantum Hypothesis ◽  
Algebraic Setting ◽  
Recent Developments ◽  
Quantum Hypothesis Testing ◽  
Non Equilibrium

We extend the mathematical theory of quantum hypothesis testing to the general W*-algebraic setting and explore its relation with recent developments in non-equilibrium quantum statistical mechanics. In particular, we relate the large deviation principle for the full counting statistics of entropy flow to quantum hypothesis testing of the arrow of time.

scholarly journals Unexpected imaginaries in valued fields with analytic structure

2013 ◽  
Vol 78 (2) ◽  
pp. 523-542 ◽  
Author(s):  
Deirdre Haskell ◽  
Ehud Hrushovski ◽  
Dugald Macpherson
Keyword(s):  
Analytic Structure ◽  
Valued Fields ◽  
Algebraic Setting

AbstractWe give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric’ sorts which suffice to code all imaginaries in the corresponding algebraic setting.

scholarly journals Linear logic in normed cones: probabilistic coherence spaces and beyond

2021 ◽  
pp. 1-40
Author(s):  
Sergey Slavnov
Keyword(s):  
Programming Languages ◽  
Linear Logic ◽  
Model Fitting ◽  
Dual Pairs ◽  
Algebraic Setting ◽  
Real Analytic Functions ◽  
Fitting In ◽  
Positive Coefficients ◽  
Probabilistic Coherence ◽  
Coherence Spaces

Abstract Ehrhard et al. (2018. Proceedings of the ACM on Programming Languages, POPL 2, Article 59.) proposed a model of probabilistic functional programming in a category of normed positive cones and stable measurable cone maps, which can be seen as a coordinate-free generalization of probabilistic coherence spaces (PCSs). However, unlike the case of PCSs, it remained unclear if the model could be refined to a model of classical linear logic. In this work, we consider a somewhat similar category which gives indeed a coordinate-free model of full propositional linear logic with nondegenerate interpretation of additives and sound interpretation of exponentials. Objects are dual pairs of normed cones satisfying certain specific completeness properties, such as existence of norm-bounded monotone weak limits, and morphisms are bounded (adjointable) positive maps. Norms allow us a distinct interpretation of dual additive connectives as product and coproduct. Exponential connectives are modeled using real analytic functions and distributions that have representations as power series with positive coefficients. Unlike the familiar case of PCSs, there is no reference or need for a preferred basis; in this sense the model is invariant. PCSs form a full subcategory, whose objects, seen as posets, are lattices. Thus, we get a model fitting in the tradition of interpreting linear logic in a linear algebraic setting, which arguably is free from the drawbacks of its predecessors.

Sign in / Sign up

Export Citation Format

Share Document