Plethystic Algebra
| dc.contributor.author | Borger, James | |
| dc.contributor.author | Wieland, Ben | |
| dc.date.accessioned | 2015-12-07T22:43:24Z | |
| dc.date.issued | 2005 | |
| dc.date.updated | 2015-12-07T11:17:59Z | |
| dc.description.abstract | The notion of a Z-algebra has a non-linear analogue, whose purpose it is to control operations on commutative rings rather than linear operations on abelian groups. These plethories can also be considered non-linear generalizations of cocommutative bialgebras. We establish a number of category-theoretic facts about plethories and their actions, including a Tannaka-Krein-style reconstruction theorem. We show that the classical ring of Witt vectors, with all its concomitant structure, can be understood in a formula-free way in terms of a plethystic version of an affine blow-up applied to the plethory generated by the Frobenius map. We also discuss the linear and infinitesimal structure of plethories and explain how this gives Bloch's Frobenius operator on the de Rham-Witt complex. | |
| dc.identifier.issn | 0001-8708 | |
| dc.identifier.uri | http://hdl.handle.net/1885/24997 | |
| dc.publisher | Academic Press | |
| dc.source | Advances in Mathematics | |
| dc.subject | Keywords: Bialgebra; Biring; Delta-ring; Lambda-ring; Plethory; Ring scheme; Symmetric function; Witt ring; Witt vector | |
| dc.title | Plethystic Algebra | |
| dc.type | Journal article | |
| local.bibliographicCitation.lastpage | 283 | |
| local.bibliographicCitation.startpage | 246 | |
| local.contributor.affiliation | Borger, James, College of Physical and Mathematical Sciences, ANU | |
| local.contributor.affiliation | Wieland, Ben, University of Chicago | |
| local.contributor.authoremail | u4260244@anu.edu.au | |
| local.contributor.authoruid | Borger, James, u4260244 | |
| local.description.embargo | 2037-12-31 | |
| local.description.notes | Imported from ARIES | |
| local.identifier.absfor | 010103 - Category Theory, K Theory, Homological Algebra | |
| local.identifier.absfor | 010101 - Algebra and Number Theory | |
| local.identifier.ariespublication | u8606170xPUB35 | |
| local.identifier.citationvolume | 194 | |
| local.identifier.doi | 10.1016/j.aim.2004.06.006 | |
| local.identifier.scopusID | 2-s2.0-18444364969 | |
| local.identifier.uidSubmittedBy | u8606170 | |
| local.type.status | Published Version |
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