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The main goal of this program is to study the Scheme theory which is the foundation for modern algebraic geometry and the Cohomology theory which is the major technique to define numerical invariants.

The audiences have to be equipped with the background on Chapter I and Chapter II (2.1~2.7) of the book “R. Hartshorne: Algebraic Geometry”.

Contents:
1. Intrinsic geometry:
    1.1 Sheaves of differential: algebraic version of differential forms
    1.2 Formal schemes: they carry information about all the infinitesimal neighborhoods.
2. Cohomology theory:
    We intend to define it by using derived functors and to compute it by introducing Cech cohomology. We also show some important vanishing theorems and combine them with Serre duality to give some applications in flat family、smooth family, including Zariski’s main theorem and base change theorem of cohomology.

Speakers: 陳宗震、郭婷婷、張茗遠、許嘉麟、莊家華

Date: June 23 - September 1, 2022

Time: Every Tuesday and Thursday, 14:00 - 16:00

Venue: Room 201, Astro-Math Building, NTU

Organizer: Prof. Hui-Wen Lin (Dept. of Mathematics, NTU & TIMS)

Available Talk List

2022-06-23 (Thu.)	Differentials 陳宗震 ( National Taiwan University )
2022-06-30 (Thu.)	On a problem of Sidon 莊家華 ( National Taiwan University )
2022-07-07 (Thu.)	Cohomology of a Noetherian Affine Scheme and Cech Cohomology 郭婷婷 ( National Taiwan University )
2022-07-14 (Thu.)	Cohomology of Projective Space and Ext Groups and Sheaves 張茗遠 ( National Taiwan University )
2022-07-21 (Thu.)	Serre duality 陳宗震 ( National Taiwan University )
2022-07-28 (Thu.)	Higher direct images and its applications 許嘉麟 ( National Taiwan University )
2022-08-05 (Fri.)	Flat Morphisms 莊家華 ( National Taiwan University )
2022-08-18 (Thu.)	Smooth morphisms 郭婷婷 ( National Taiwan University )
2022-08-23 (Tue.)	Formal schemes 張茗遠 ( National Taiwan University )
2022-08-25 (Thu.)	The theorem on formal functions 陳宗震 ( National Taiwan University )