Computing homological residue fields in algebra and topology
نویسندگان
چکیده
We determine the homological residue fields, in sense of tensor-triangular geometry, a series concrete examples ranging from topological stable homotopy theory to modular representation finite groups.
منابع مشابه
Categories and Homological Algebra
The aim of these Notes is to introduce the reader to the language of categories with emphazis on homological algebra. We treat with some details basic homological algebra, that is, categories of complexes in additive and abelian categories and construct with some care the derived functors. We also introduce the reader to the more sophisticated concepts of triangulated and derived categories. Ou...
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These lectures are a quick primer on the basics of applied algebraic topology with emphasis on applications to data. In particular, the perspectives of (elementary) homological algebra, in the form of complexes and co/homological invariants are sketched. Beginning with simplicial and cell complexes as a means of enriching graphs to higher-order structures, we define simple algebraic topological...
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= convex hull of {a0, . . . , an}. The points a0, . . . , an are geometrically independent if a1 − a0, . . . , an − a0 is a linearly independent set over R. Note that this is independent of the order of a0, . . . , an. In this case, we say that the simplex a0 . . . an is n -dimensional, or an n -simplex. Given a point Pn i=1 λiai belonging to an n-simplex, we say it has barycentric coordinates ...
متن کاملSome homological algebra
1.1 Adjoint functors Let C and D be categories and let f∗ : C → D and f∗ : D → C be functors. Then f∗ is a right adjoint to f∗ and f∗ is a left adjoint to f∗ if, for each D ∈ D and C ∈ C there is a natural vector space isomorphism HomC(fD,C) Φ −→HomD(D, f∗C). For C ∈ C and D ∈ D define τC = Φ(idf∗C) ∈ HomC(ff∗C,C) and φD = Φ(idf∗D) ∈ HomD(D, f∗fD). In general τC and φD are neither injective nor...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2021
ISSN: ['2330-1511']
DOI: https://doi.org/10.1090/proc/15412