Jannsen, Uwe (2010) Weights in arithmetic geometry. JAPANESE JOURNAL OF MATHEMATICS, 5 (1). pp. 73-102. ISSN 0289-2316,
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The concept of weights on the cohomology of algebraic varieties was initiated by fundamental ideas and work of A. Grothendieck and P. Deligne. It is deeply connected with the concept of motives and appeared first on the singular cohomology as the weights of (possibly mixed) Hodge structures and on the etale cohomology as the weights of eigenvalues of Frobenius. But weights also appear on algebraic fundamental groups and in p-adic Hodge theory, where they become only visible after applying the comparison functors of Fontaine. After rehearsing various versions of weights, we explain some more recent applications of weights, e.g. to Hasse principles and the computation of motivic cohomology, and discuss some open questions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | SEMI-STABLE REDUCTION; ADIC ETALE COHOMOLOGY; CRYSTALLINE COHOMOLOGY; FINITE-FIELDS; K-THEORY; VARIETIES; SINGULARITIES; RESOLUTION; THREEFOLDS; FORMS; weights; etale cohomology; Hasse principles |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Uwe Jannsen |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 03 Aug 2020 08:43 |
| Last Modified: | 03 Aug 2020 08:43 |
| URI: | https://pred.uni-regensburg.de/id/eprint/24915 |
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