Berkeley Lectures on p-adic Geometry (eBook)

Peter Scholze, Jared Weinstein (Autoren)

eBook Download: PDF

2020
264 Seiten
Princeton University Press (Verlag)
978-0-691-20215-0 (ISBN)

Infos

Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of ';diamonds,' which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field.This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.

Produkt-Details

• Erscheint lt. Verlag: 26.5.2020
• Reihe/Serie: Annals of Mathematics Studies
• Reihe/Serie: Annals of Mathematics Studies
• Zusatzinfo: 5 b/w illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: abelian variety • Adic spaces • affine Grassmannians • Affine space • Algebraically closed field • Algebraic Geometry • Algebraic space • analytic geometry • Antiderivative • Archimedean property • automorphism • Base change • bijection • C0 • category of rings • Characterization (mathematics) • Closed immersion • cohomology • cohomology of local systems • Compact space • conjecture • conjugacy class • Connected component (graph theory) • Crystalline Cohomology • deformation theory • Diagram (category theory) • Dieudonné theory • Disjoint union • Divisible group • Drinfeld’s lemma • equivalence class • Equivalence of Categories • Exceptional isomorphism • existential quantification • Exterior algebra • Facet (geometry) • Fargues-Fontaine curve • fiber bundle • Field of fractions • Finitely presented • Flag varieties • Formal scheme • formal schemes • functor • galois cohomology • Generic point • Geometry • Group (mathematics) • Homeomorphism • Homomorphism • Ideal (ring theory) • Injective function • Integral element • Integral Models • Inverse limit • Inverse System • isomorphism class • Limit (category theory) • Linear algebraic group • Mathematical Induction • Mathematical Proof • Maximal compact subgroup • Module (mathematics) • moduli space • Morphism • Morphism of schemes • Neighbourhood (mathematics) • Newton Polygon • Open set • p-adic Hodge theory • P-adic number • perfectoid • perfectoid rings • Pre-adic spaces • Presheaf (category theory) • Profinite group • projective module • projective space • projective variety • Pullback (category theory) • Pushout (category theory) • Quasi-projective variety • reductive group • residue field • Ring of integers • Set (mathematics) • Sheaf (mathematics) • shimura varieties • Shimura variety • Special case • spectrum of a ring • Stein factorization • subcategory • Subset • Surjective function • Tate module • tensor product • Theorem • theory • topological group • Topological ring • Topological space • Topology • Torsor (algebraic geometry) • torsors • Totally disconnected space • Total order • transcendence degree • Upper half-plane • Valuation ring • vector bundle • Vector Bundles • v-sheaves • v-topology • Witt vector • Zariski topology
• ISBN-10: 0-691-20215-X / 069120215X
• ISBN-13: 978-0-691-20215-0 / 9780691202150