On two examples by Iyama and Yoshino

AbstractIn a recent paper, Iyama and Yoshino considered two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen–Macaulay modules in terms of linear algebra data. In this paper, we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov’s result on the graded singularity category.

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The p-adic Simpson Correspondence (AM-193)

10.23943/princeton/9780691170282.001.0001 ◽

2017 ◽

Cited By ~ 4

Author(s):

Ahmed Abbes ◽

Michel Gros ◽

Takeshi Tsuji

Keyword(s):

Fundamental Group ◽

Linear Algebra ◽

General Framework ◽

Hodge Theory ◽

Higgs Bundles ◽

Smooth Variety ◽

Trivial Representation ◽

New Approaches ◽

New Family ◽

Systematic Development

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra—namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches. It mainly focuses on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The book shows the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the book contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost étale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored.

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Beyond autism: Challenging unexamined assumptions about social motivation in typical development

Behavioral and Brain Sciences ◽

10.1017/s0140525x18002273 ◽

2019 ◽

Vol 42 ◽

Author(s):

Karen Bartsch ◽

David Estes

Keyword(s):

Social Interest ◽

Social Motivation ◽

Typical Development ◽

Typically Developing ◽

New Approaches

Abstract In challenging the assumption of autistic social uninterest, Jaswal & Akhtar have opened the door to scrutinizing similar unexamined assumptions embedded in other literatures, such as those on children's typically developing behaviors regarding others’ minds and morals. Extending skeptical analysis to other areas may reveal new approaches for evaluating competing claims regarding social interest in autistic individuals.

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