WebBackground. Perfectoid spaces are a class of spaces in p-adic arithmetic geometry introduced in 2012 by Peter Scholze in his PhD thesis. Very roughly speaking, these spaces are modeled by (spectra attached to) Z p-algebras whose mod p reductions have all p-power roots. Despite their youth, these spaces have had stunning applications to WebIn this school, we intend to understand connections between the arithmetic theory of modular forms and new developments in p-adic Hodge theory that grew from the breakthrough work of Peter Scholze on perfectoid spaces (see P. Scholze "Perfectoid spaces" Publ. Math. de l’IHES 116 (2012)). p-adic methods play a key role in the study of ...
Formalising perfectoid spaces - arXiv
Web23. jan 2024 · Perfectoid spaces are this year's subject for the Arizona Winter School (link) and, as preparation, I am currently trying to understand the subject better. ... Apart from all the written sources, there are six videos of Peter Scholze's lectures at the IHÉS in 2011 on Perfectoid Spaces and the Weight-Monodromy Conjecture : WebPERFECTOID SPACES PETER SCHOLZE Abstract. We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings’ almost purity … phil beadle teacher
What is a brief description of Peter Scholze
Web10. aug 2012 · P. Scholze, p-adic Hodge theory for rigid-analytic varieties, arXiv:1205.3463, 2012. S. W. Shin, Galois representations arising from some compact Shimura varieties, … WebIn recognition of the transformative impact perfectoid spaces have had on the field of arithmetic geometry, Scholze was awarded a Fields Medal in 2024. This book, originating … Web1. aug 2024 · Scholze continues to explore perfectoid spaces, but he has also branched out into other areas of mathematics touching on algebraic topology, which uses algebra to study shapes. “Over the course of the last year and a half, Peter has become a complete master of the subject,” Bhatt said. “He changed the way [the experts] think about it.” phil beadle the unteachables