Download E-books Kolyvagin Systems PDF

By Barry Mazur

Because their creation through Kolyvagin, Euler structures were utilized in a number of vital functions in mathematics algebraic geometry. For a $p$-adic Galois module $T$, Kolyvagin's equipment is designed to supply an higher sure for the scale of the Selmer staff linked to the Cartier twin $T^*$. Given an Euler method, Kolyvagin produces a set of cohomology sessions which he calls 'derivative' sessions. it truly is those spinoff periods that are used to certain the twin Selmer crew. the place to begin of the current memoir is the statement that Kolyvagin's platforms of spinoff sessions fulfill better interrelations than have formerly been well-known. We name a process of cohomology sessions fulfilling those greater interrelations a Kolyvagin system.We exhibit that the additional interrelations supply Kolyvagin structures an engaging inflexible constitution which in lots of methods resembles (an enriched model of) the 'leading time period' of an $L$-function. by way of utilising the additional stress we additionally end up that Kolyvagin platforms exist for lots of attention-grabbing representations for which no Euler approach is understood, and additional that there are Kolyvagin platforms for those representations which provide upward thrust to specific formulation for the dimensions of the twin Selmer workforce, instead of simply higher bounds.

Show description

Read or Download Kolyvagin Systems PDF

Best Algebraic Geometry books

A Concise Course in Algebraic Topology (Chicago Lectures in Mathematics Series)

Algebraic topology is a simple a part of glossy arithmetic, and a few wisdom of this sector is vital for any complicated paintings in terms of geometry, together with topology itself, differential geometry, algebraic geometry, and Lie teams. This booklet presents an in depth remedy of algebraic topology either for lecturers of the topic and for complicated graduate scholars in arithmetic both focusing on this quarter or carrying on with directly to different fields.

The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra (Graduate Texts in Mathematics)

First textbook-level account of simple examples and strategies during this region. compatible for self-study through a reader who understands a bit commutative algebra and algebraic geometry already. David Eisenbud is a well known mathematician and present president of the yank Mathematical Society, in addition to a profitable Springer writer.

The Geometry of Schemes (Graduate Texts in Mathematics)

Grothendieck’s attractive thought of schemes permeates smooth algebraic geometry and underlies its purposes to quantity idea, physics, and utilized arithmetic. this easy account of that conception emphasizes and explains the common geometric options in the back of the definitions. within the ebook, options are illustrated with primary examples, and particular calculations exhibit how the structures of scheme idea are conducted in perform.

Geometric Algebra

This vintage textual content, written via one of many top-rated mathematicians of the 20 th century, is now on hand in a reasonable paperback variation. Exposition is based at the foundations of affine geometry, the geometry of quadratic types, and the constitution of the final linear staff. Context is broadened by means of the inclusion of projective and symplectic geometry and the constitution of symplectic and orthogonal teams.

Extra resources for Kolyvagin Systems

Show sample text content

Rated 4.67 of 5 – based on 6 votes