On the Kolyvagin cup product
نویسندگان
چکیده
منابع مشابه
Cup product and intersection
This is a handout for my algebraic topology course. The goal is to explain a geometric interpretation of the cup product. Namely, if X is a closed oriented smooth manifold, if A and B are oriented submanifolds of X, and if A and B intersect transversely, then the Poincaré dual of A∩B is the cup product of the Poincaré duals of A and B. As an application, we prove the Lefschetz fixed point formu...
متن کاملThe Universal Kolyvagin Recursion Implies the Kolyvagin Recursion
Let Uz be the universal norm distribution and M a fixed power of prime p, by using the double complex method employed by Anderson, we study the universal Kolyvagin recursion occurred in the canonical basis in the cohomology group H(Gz ,Uz/MUz). We furthermore show that the universal Kolyvagin recursion implies the Kolyvagin recursion in the theory of Euler systems. One certainly hopes this coul...
متن کاملIntroduction to Kolyvagin systems
Since their introduction by Kolyvagin in [Ko], Euler systems have been used in several important applications in arithmetic algebraic geometry. For a p-adic Galois module T , Kolyvagin’s machinery is designed to provide an upper bound for the size of a Selmer group associated to the Cartier dual of T . Kolyvagin’s method proceeds in three steps. The first step is to establish an Euler system as...
متن کاملExtended higher cup-product Chern-Simons theories
It is well known that the proper action functional of (4k+ 3)-dimensional U(1)-Chern-Simons theory including the instanton sectors is given on gauge equivalence classes of fields by the fiber integration of the cup product square of classes in degree-(2k + 2) differential cohomology. We first refine this statement from gauge equivalence classes to the full higher smooth moduli stack of fields, ...
متن کاملFinite Groups Acting Linearly: Hochschild Cohomology and the Cup Product
When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics. Its Hochschild cohomology predicts var...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01777-7