p-adic Hodge theory and its application

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740001
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Hokkaido University
• Principal Investigator: MORITA Kazuma 北海道大学, 理学(系)研究科(研究院), 助教 (40548187)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: p-adic Hodge theory / algebraic cycle / elliptic curve

Outline of Final Research Achievements

(1). In the higher dimensional p-adic Hodge theory, I generalized the p-adic monodromy theorem due to L.Berger. (2). It is known that the mixed Hodge structure due to P.Deligne cannot enough information about algebraic cycles and I constructed the new category which can capture the information about algebraic cycles. (3). I showed that rational points on arithmetic elliptic curves which are discrete objects could behave as continuous objects. (4). Based on the study on (2) and (3), I gave some observations on theoretical physics.

Free Research Field

整数論