By Hiroyuki Yoshida

ISBN-10: 0821834533

ISBN-13: 9780821834534

ISBN-10: 2101998416

ISBN-13: 9782101998417

ISBN-10: 3119795615

ISBN-13: 9783119795616

ISBN-10: 3419323603

ISBN-13: 9783419323601

ISBN-10: 4519823153

ISBN-13: 9784519823152

The principal topic of this publication is an invariant connected to a terrific category of a unconditionally genuine algebraic quantity box. This invariant offers us with a unified figuring out of sessions of abelian kinds with advanced multiplication and the Stark-Shintani devices. it is a new standpoint, and the booklet includes many new effects with regards to it. to put those ends up in right standpoint and to provide instruments to assault unsolved difficulties, the writer offers systematic expositions of primary themes. hence the ebook treats the a number of gamma functionality, the Stark conjecture, Shimura's interval image, absolutely the interval image, Eisenstein sequence on $GL(2)$, and a restrict formulation of Kronecker's kind. The dialogue of every of those themes is improved by way of many examples. the vast majority of the textual content is written assuming a few familiarity with algebraic quantity idea. approximately thirty difficulties are incorporated, a few of that are particularly demanding. The e-book is meant for graduate scholars and researchers operating in quantity conception and automorphic types

Show description

Read or Download Absolute CM-periods PDF

Best algebraic geometry books

Read e-book online Algebraic Curves over Finite Fields PDF

During this tract, Professor Moreno develops the idea of algebraic curves over finite fields, their zeta and L-functions, and, for the 1st time, the speculation of algebraic geometric Goppa codes on algebraic curves. one of the functions thought of are: the matter of counting the variety of strategies of equations over finite fields; Bombieri's facts of the Reimann speculation for functionality fields, with effects for the estimation of exponential sums in a single variable; Goppa's idea of error-correcting codes produced from linear structures on algebraic curves; there's additionally a brand new facts of the TsfasmanSHVladutSHZink theorem.

Read e-book online An invitation to arithmetic geometry PDF

During this quantity the writer provides a unified presentation of a few of the fundamental instruments and ideas in quantity thought, commutative algebra, and algebraic geometry, and for the 1st time in a ebook at this point, brings out the deep analogies among them. The geometric point of view is under pressure through the booklet.

Birationally Rigid Varieties: Mathematical Analysis and by Aleksandr Pukhlikov PDF

Birational stress is a impressive and mysterious phenomenon in higher-dimensional algebraic geometry. It seems that yes usual households of algebraic kinds (for instance, three-d quartics) belong to an analogous category variety because the projective area yet have considerably assorted birational geometric homes.

Extra resources for Absolute CM-periods

Example text

Verify that the same is true over the algebraic closure of any finite field Fp, p # 7. What can you say about the automorphism group of the singular curve over the finite field F7? 3. Show that the automorphism group of the curve y 2 — y = x 3 is isomorphic to SL2(F3). ) 4. Consider the plane projective curve x* + y* + z 4 over a field F of characteristic different from 2. Let G, = S3 be the group of permutations of the coordinates in P2 and G2 the group generated by multiplication of coordinates by roots of unity.

To show this we shall construct these elements step by step. For zx we take any element in Kx with vx(zx) ¥^0. ,n)e Q": £ rtv,(*i) = oj =ft- 1. =i r,i;,(zk+1) / 0. , r») e Q*: £ wfa) = 0,1 < ; w e have —d d for for i=k i =fc k.

In fact think of K as the subset of principal pre-adeles in A and for x e K and u> e £%/jt(D) put xft)(r) = co(xr) for any r e A/(A (D) + K). K/k(D - (x)). The following properties are immediate consequences of the definitions: for x, y e K and co, co' e i^ /jk we have (i) (xy)a> = x(yco), (ii) (x + y)a> = xa> + yu> (iii) x(w + a)') = xo) + xw'. This shows that Q^ /t is a vector space over K. We have the following more precise result. 4 Let K be the function field of the curve C with field of constants k.

Download PDF sample

Absolute CM-periods by Hiroyuki Yoshida

by Robert

Rated 4.52 of 5 – based on 3 votes